If you're looking to go super cheap and don't mind a little effort, you can grab one of the inexpensive frames from Walmart/Target/Michael's and add some hardware yourself. You'll want to add a piece of glassine or some other acid-free backing so the art isn't resting on the cardboard that came with the frame. Then, grab yourself some spacers, and then put your art in. Let the record show that both of the items I linked to can be found in smaller, less expensive packs.
The key here, and especially with foil, is not letting the art touch the glass/plexi or backing of that inexpensive frame. The acid-free backing and spacers will help prevent any damage from merely sitting in the frame. If you haven't already broke the bank, look into UV protected glass or plexi to swap into the inexpensive frame. If not, try to hang it away from direct sunlight, as that will eventually cause some issues, but years down the road.
... so the sleeves are the issue. What did you buy? Something like this is what you need. I've got one almost entirely filled with 18x24 concert posters and they all fit without sticking out at all.
If you cut the poster it's value is greatly diminished and if you decide to put it on the wall someday, it won't fit in a standard 18x24 frame... each of your posters is likely more than the cost of a new portfolio, get a better one.
I use a portfolio as well; I've had it for years with no issues. The outer cover is larger than the sleeves and it's made of a hard plastic. When it's closed, it's tough to bump any corners.
To flatten, I use my dining room table to lay the poster down and then put some glass coasters on each corner. If I remember to do it within a day or two of the show, it only takes a day or two to stay pretty flat and then it slides right in.
Here's a link to the one I bought: https://www.amazon.com/Itoya-Profolio-Evolution-Presentation-Display/dp/B01M0L2YOV/
That price is ridiculous, I'm sure you can finder it cheaper elsewhere.
You may be able to find one cheaper if you google around, but they get the job done. If money is no object to you, check out the Baroque portfolios. They are well built and durable (not that the itoya's aren't), but they cost a LOT more and there is often a wait time before they have enough to ship out.