I just got a house and my score is 551, it was 420 last fall. Like you I'm a single mom and make plenty of money to afford a house, but just don't have the credit (mine was my daughters hospital bills/no credit due to the hospital bills). Obviously credit repair is an important issue, but if you need to find a place in one month then look at rent to own, That is how I got my house, and it is a turn key house, I don't even have to paint. I am able to rent this house month to month as long as I want and I have the price locked in. I can "try on the house" and make sure it's going to fit for us, and there are no major issues, and can move out if I want without being out any money or being stuck trying to sell a house. My downpayment is only $3000, and my monthly payment is $600/month and I gross $3000/mo. In a year when I am able to get financed my money has already gone toward the purchase price, and I don't have to relocate my kids again. Also, if for some reason I can't get financed in a year then they will do a land contract.
Also, (making that much money you're probably looking at a nicer house than mine). My house is valued at $83k, and I'm getting it for $69k, so, it's not way overpriced and I live pretty much out in the boonies with the cows and the cornfields, so I'm sure there is alot more inventory for rent to own where you're at.
Only other option I had was to go with a manual underwriter, they don't look at your score, just if you've paid your bills on time for the past year (I think they just look at housing type bills mainly, because they didn't care if I paid my hospital bills or student loans). Maybe try Flagstar bank if you go that route. Hope this helps!