I use a Nordic Ware cooker. I've been using them for years, and have perfected the timing for my oven so the eggs are consistently the way I like them - not overdone. Total time if I start with hot water is 11 minutes.
They are usually easy to peel, but from my reading, it seems that it depends a lot on how fresh the eggs are - the fresher they are, the harder to peel.
I like this microwave egg boiler. It takes a while dial in the right time with your microwave since they vary, but once you do, it's easy hard boiled eggs when you're without a stove.
I use this
Gets them done in 7 minutes in the microwave. Way faster than on the stove for me, it takes at least that for me to get water boiling on my stove.
Here is a link for it on Amazon. Nordic Ware Microwave Egg Boiler https://www.amazon.com/dp/B0007M2BN0/ref=cm_sw_r_sms_apa_i_z7EbEbYV5JWMY
My electric kettle and my microwave egg boiler. I've had the egg thing for 11 years and I still use it all the time.
Love this microwave egg steamer.
I'm not lifting ~~like I should~~ at all, but I've got this stupid thing that makes cooking and eating eggs easy af. https://www.amazon.com/Nordic-Ware-Microwave-Egg-Boiler/dp/B0007M2BN0
I use this a lot: https://www.amazon.com/Nordic-Ware-Microwave-Egg-Boiler/dp/B0007M2BN0/ref=sr_1_4?ie=UTF8&qid=1476929651&sr=8-4&keywords=microwave+cooker+eggs
Here's an excellent microwave breakfast: http://cavemanketo.com/hotel-room-breakfast/
A whole page of microwave cookers: https://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Daps&field-keywords=microwave+cooker
You can use the rice cooker for steaming veg, and for making soups/stews. You can use the Stoneware thingy for making single custards (basically egg and cream) or one minute muffins (usually protein powder, egg, cream, butter, plus whatever you like), or for single-servings of anything at all.
I've never used the grill, but I have a friend who swears by hers.
I still think you should consider getting a $15 slow cooker... but that's up to you.
Microwave breakfast here: http://cavemanketo.com/hotel-room-breakfast/
More low fuss/no fuss ideas here: http://ketodietapp.com/Blog/post/2014/01/17/7-Day-Grab-Go-KetoPaleo-Diet-Plan
Excellent (and cheap) microwave egg cooker for hard boiled eggs: https://www.amazon.com/Nordic-Ware-Microwave-Egg-Boiler/dp/B0007M2BN0
There are a zillion recipes for mug cakes (literally cooked in a coffee mug, in a microwave, in about a minute. I generally make them with a scoop of protein powder, an egg, a bit of cream, a bit of baking powder if I have it, then whatever for flavoring (I'm fond of giant spoons of baking chocolate plus a bit of sweetener.) Here's a pretty good collection to start with: http://alldayidreamaboutfood.com/2015/03/low-carb-mug-cake-recipes.html
Make some chia pudding: 1/4c chia seeds, 1 cup liquid stuff (I generally use sugar free chocolate almond milk) plus whatever else you want. A scoop of protein. A raw egg. A blog of cocoa powder plus a bit of sweetener. Whatever. Let it sit overnight and it turns into something like a tapioca pudding, but low in carbs and high in nutrition. Very good.
If that'll get you started, by all means come back and ask for more.
Also, don't underestimate Google. It'll find a recipe for keto rhubarb, or keto eggs, or keto protein shakes or whatever. Also, keto + microwave + whatever will often work pretty well.
You can get a microwave egg boiler, too. Stupid-simple.
But if it helps, here's a so-so picture of a page in a book called 'Modernist Cuisine at Home' that has great photos of boiled eggs after various amounts of heat -- it might be a helpful visual guide for you? You're just overcooking, and not stopping the cooking process quickly enough; I'd just be brave and drain your pot, and start blasting the eggs with cold water, way earlier than you think you should. If you end up with soft boiled, be slightly less aggressive. I think I do about 9 minutes -- it's usually for salads -- and then out, and right into the cold running water.
Very fresh eggs are a pain to peel. Cheap's fine.
http://www.amazon.com/Nordic-Ware-64802-Microwave-Boiler/dp/B0007M2BN0
The one I use is similar to that
Hard boiled eggs are indeed awesome, I just need to have the foresight to boil them in advance. On that topic, This doohickey has been a God-send.
My mom has one of these, which means you can hard boil eggs in the microwave.
I got this on sale for $4.99 and it hard boils eggs perfectly
I microwave eggs in their shell all the time. You are just doing it wrong. Try this.