Firstly, where have you been looking? I recently refi'd (a little different than a new purchase, admittedly) but had a lower score than yours, and was able to secure an 8.5% 30yr conventional at 95% LTV, with minimal effort / searching. Not the greatest rate, but pretty good for a score in the mid-5's. PM me if you want a referral, or check around some more...
You say you have a couple credit cards that you "just paid off". The two questions here are, how close to the limits were they, and have those zero balances been reported to the bureaus yet (and thus factored into your 577 score)? I recently paid off my cards too, after being close to max, and the jump in my score just from doing that was pretty amazing.
Best case scenario, you had a high utilization %, and they have not yet reported. In this case, just be patient for a few months, let those balances and your score update, and you should then be close to 600 or better, at which point you shouldn't have any trouble getting financing (ableit at an increased rate).
If not, some of the other advice makes sense... take some of your savings and pay off the most recent collections. Those are the ones that are having the biggest impact on your score, and what those lenders could be eyeing as potential issues, which is likely, since even with a 577, it should be relatively easy to find a sub-prime lender (just be REAL careful of the terms, avoid ARMs at all costs, and all that.)
And congrats on conquering the cancer. I work for an organization that deals with cancer research and treatment, so it's good to see someone overcoming it