I'm not sure what exactly you are looking for, but I found several with a quick search. This one looks like one that would do what you want. Still I hope you're handy with tools, this one needs to be assembled.
https://www.amazon.com/Agri-Fab-45-0299-48-Inch-Plug-Aerator/dp/B000K6DZDI
The agri-fab weighs 90 lbs plus whatever you place on top for bricks.
That is more than strong enough to nuke your lawn. I also think it would be best to nuke it all and start fresh. Keep in mind to wear boot covers and protective equipment when spraying - try to not walk in the areas you sprayed. I highly recommend mowing or string trimming it all really short before you do it. Preferably with a bagger so you can remove most of the material. Then as the lawn dies you will rake out the dead stuff and re apply poison as needed.
You should gather your supplies for re seeding and fertilizing now too, in my opinion. If you spray down and kill it off, but don't reseed for weeks, then you're going to end up with a yard full of weeds growing again. Make sure you check the label and find out when reseeding is appropriate after putting your chemical down to kill everything, because you don't want to waste hundreds on seed and fert.
This is what I would do, and in which order for a complete overhaul:
Mow as short as possbile, bagging or raking clippings and remove them.
Put down your poison to kill everything you want to remove.
Rake dead material as needed, try to get as much out as possible.
Re-apply your Glyphosate if needed to finish off the lawn; make sure to pay attention to how much time you need between killing and reseeding.
Core aerate your lawn by paying someone to come do it, renting one, or buying one. I recommend https://www.amazon.com/Agri-Fab-45-0299-48-Inch-Plug-Aerator/dp/B000K6DZDI for a pull behind one, it works great.
Top dress your lawn with a soil/compost mixture. You can cover up the little bits of organics you missed with raking. A lot of them are a sandy soil mixed with an organic compost being manure or other choice material. You only have to put it down as this as 1/4", and can take this time to level uneven spots in your lawn. Apply to your lawn and rake it smooth. Make sure to use a top dressing suitable for your soil. Try to stay away from new mulch and new compost, because they tend to generate a lot of heat that will hurt your germination rates.
Find out what type of grass does best for you - a creeping red fescue may do well under those trees. Any Sun and Shade mix should suffice for areas that see any sun at all. If not you can go with a dense shade mix. Just do a little research, ask some local agriculture or home improvement stores for help.
Apply your seed with a broadcast spreader that is appropriate for your lawn size, they can be picked up at a hardware or home improvement store. Follow the seeding instructions on the labels, not all seed is the same; and all seed doesn't go down at the same rates. If you put down seed too thick, nothing will survive - you can always reseed patchy areas.
Rake seed gently into your top dressing. Put down seed per instructions if you missed any spots.
Apply a starter fertilizer with weed control - Scott's works very well in my experience. Make sure it's safe for seedlings.
Water the fertilizer into the lawn.
Keep your seed watered until your seedlings produce and get a few inches tall. This make take 10-40 days and it depends on the type of grass you plant. You do not need to water so much that there would be standing water in your lawn. Just keep the seeds and soil damp. I prefer to water in the morning before sun rise and mid day, and the nights are covered with a heavy dew.
Mow after your seedlings reach 3 inches tall. Keep in mind that the roots are still weak and it doesn't hurt to baby the grass for a while.
You can apply something like Milorganite or other organic fertilizer. I have heard to wait until your grass is mowed over a few times if you're gonna use a synthetic fertilizer at this point.
Apply a pre-emergent to your lawn in the spring season to prevent crabgrass breakout. A weed killer with Quinclorac will kill crabgrass if it is still a young plant, but won't do much for a matured plant.
Spot treat for weeds with a grass safe concentrate as needed through the early summer months.
Mow your lawn at recommended heights. Tall, thick grass prevents weeds from being able to grow through.
Edit: Submitted before finished post.
If the moles are destroying your lawn, you do want to get rid of them before you spend a lot of time and money on this project. Usually you can put down a repellent to keep them away, just follow instructions. They can also cause them to move where you don't want to go if you apply it incorrectly. Trapping if you can is probably the easiest to get them out if you're not poisoning them.
I live in the Northern US and my crabgrass is starting to die now and we haven't had any frost. It seems like it has started to die once the seed heads have gone out. It's like most annual flowers are that you can buy in a hanging basket; they grow, bloom and go to seed before they die.
That is more than strong enough to nuke your lawn. I also think it would be best to nuke it all and start fresh. Keep in mind to wear boot covers and protective equipment when spraying - try to not walk in the areas you sprayed. I highly recommend mowing or string trimming it all really short before you do it. Preferably with a bagger so you can remove most of the material. Then as the lawn dies you will rake out the dead stuff and re apply poison as needed.
You should gather your supplies for re seeding and fertilizing now too, in my opinion. If you spray down and kill it off, but don't reseed for weeks, then you're going to end up with a yard full of weeds growing again. Make sure you check the label and find out when reseeding is appropriate after putting your chemical down to kill everything, because you don't want to waste hundreds on seed and fert.
This is what I would do, and in which order for a complete overhaul:
Mow as short as possbile, bagging or raking clippings and remove them.
Put down your poison to kill everything you want to remove.
Rake dead material as needed, try to get as much out as possible.
Re-apply your Glyphosate if needed to finish off the lawn; make sure to pay attention to how much time you need between killing and reseeding.
Core aerate your lawn by paying someone to come do it, renting one, or buying one. I recommend https://www.amazon.com/Agri-Fab-45-0299-48-Inch-Plug-Aerator/dp/B000K6DZDI for a pull behind one, it works great.
Top dress your lawn with a soil/compost mixture. You can cover up the little bits of organics you missed with raking. A lot of them are a sandy soil mixed with an organic compost being manure or other choice material. You only have to put it down as this as 1/4", and can take this time to level uneven spots in your lawn. Apply to your lawn and rake it smooth. Make sure to use a top dressing suitable for your soil. Try to stay away from new mulch and new compost, because they tend to generate a lot of heat that will hurt your germination rates.
Find out what type of grass does best for you - a creeping red fescue may do well under those trees. Any Sun and Shade mix should suffice for areas that see any sun at all. If not you can go with a dense shade mix. Just do a little research, ask some local agriculture or home improvement stores for help.
Apply your seed with a broadcast spreader that is appropriate for your lawn size, they can be picked up at a hardware or home improvement store. Follow the seeding instructions on the labels, not all seed is the same; and all seed doesn't go down at the same rates. If you put down seed too thick, nothing will survive - you can always reseed patchy areas.
Rake seed gently into your top dressing. Put down seed per instructions if you missed any spots.
Apply a starter fertilizer with weed control - Scott's works very well in my experience. Make sure it's safe for seedlings.
Water the fertilizer into the lawn.
Keep your seed watered until your seedlings produce and get a few inches tall. This make take 10-40 days and it depends on the type of grass you plant. You do not need to water so much that there would be standing water in your lawn. Just keep the seeds and soil damp. I prefer to water in the morning before sun rise and mid day, and the nights are covered with a heavy dew.
Mow after your seedlings reach 3 inches tall. Keep in mind that the roots are still weak and it doesn't hurt to baby the grass for a while.
You can apply something like Milorganite or other organic fertilizer. I have heard to wait until your grass is mowed over a few times if you're gonna use a synthetic fertilizer at this point.
Apply a pre-emergent to your lawn in the spring season to prevent crabgrass breakout. A weed killer with Quinclorac will kill crabgrass if it is still a young plant, but won't do much for a matured plant.
Spot treat for weeds with a grass safe concentrate as needed through the early summer months.
Mow your lawn at recommended heights. Tall, thick grass prevents weeds from being able to grow through.
Edit: Submitted before finished post.
If the moles are destroying your lawn, you do want to get rid of them before you spend a lot of time and money on this project. Usually you can put down a repellent to keep them away, just follow instructions. They can also cause them to move where you don't want to go if you apply it incorrectly. Trapping if you can is probably the easiest to get them out if you're not poisoning them.
I live in the Northern US and my crabgrass is starting to die now and we haven't had any frost. It seems like it has started to die once the seed heads have gone out. It's like most annual flowers are that you can buy in a hanging basket; they grow, bloom and go to seed before they die.