Ok, since you need to work this all out by Tuesday, this is my advice.
Go to the mixer, see if you you do "connect" with anyone there. Maybe you will meet some fantastic people! Who knows. I am sure more then one person there is in the same boat as you, maybe you will even meet a fellow Aspie, as the stats now point to the plausability in your situation you are not the only one.
If the mixer goes horribly, go to a doctor, and get a note regarding your condition, your stress over this situation, and request assistance with housing. Either they need to find you a room mate you find agreeable, or they need to BEND the rules, to give you a private room or let you live off campus.
Remember, this is a disability in the eyes of the law. It is just like if you where in a wheelchair and needed a ramp to the dorm. They can't insist you live in the dorm, if they don't provide a ramp right? They need to help you fit into the dorm. If they cannot (for example, there is no way to install a ramp if you where disabled) then they need to allow an off campus move to a place that has a ramp!
Sure, if you where paralysed, you may be able to "throw yourself out of the chair, throw the chair over your head up the stairs ahead of you, crawl up the stairs dragging your back end behind you and then struggle to get back into the chair once you get to the top!" But, that sounds ridiculous, no institution would EVER DEMAND you do that, or even want you to! And if they did, laws in the western world prohibit it!
Asking you to find a partner if one cannot be found and not offering accomidation or assistance is demeaning and a breach of your rights.
By all means, go to the mixer, work the process, do your best to "try" and find a partner, at this late date, you can't get out of that. But don't feel forced to room with someone you would rather not, or suffer the stress of walking away empty handed and feeling desperate!
If the mixer works, great, if not, persue the disability angle to get an accomidation. I agree, being "on" 100% of the time in college with nowhere for down time is not going to be easy on you!