If I settle a collections debt or pay the balance down under $2,085, will I qualify for a grad PLUS loan?

So, I'm in a really tight spot right now about to graduate undergrad with a B. S in Biology and Psychology, with the intention of going to grad school to become a physician assistant. I have a joint collections account in my name for $5k from an apartment lease due to my parent forging my signature and using my social security. On top of this she also used my info on a few credit cards which I've slowly been paying off and she no longer has access to. I changed my SSN as well. After disputing multiple times with each bureau, I was told my only option would be to file a police report--which having an immigrant mother, I just cannot do. She has told me point blank that she has no intention of paying off the balance, so it's left purely to me, and it's also the entirety of my credit history aside from my car note. I know that if I work two jobs full time over the summer, I could make about 2k-3k and do a settlement, also once I receive the grad loan, I will just take out a bit more and pay off the remaining balances and live below my means throughout grad school, letting my credit have time to recover over the next 3 years. However, this is all banked on the idea that student aid accepts settlement letters instead of paid in full letters. I've worked so hard to put myself through school and get out of that situation and I just hate that this could be how it ends for me, I really do want to be a P. A more than anything.

Updates
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Thanks everyone whose replied so far, I do want to add that I know the most logical route is to seek police, but for my own spirit I cannot do something that will potentially harm my mother, despite everything she's done. I don't really have money for an attorney, but I will try and get a free consultation. If anyone has had adverse credit when they applied for a grad plus loan any info would be helpful.
If I settle a collections debt or pay the balance down under $2,085, will I qualify for a grad PLUS loan?
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