Gib, this is something that i think you might be able to get done with a little more $$ - keep shopping lenders and find someone who has a purchase / renovation loan -- what you want to look for is someone who will offer the highest loan to value % so you will have to put down as little $$ as possible, and then you can see if you can make something work - basically at a purchase price of 310 you're looking at a 340k acquisition cost (always goos to overestimate on renovations), so based on what kind of max ltv% you can find you will know what you need - you will also have to take into account closing costs, etc.
Another potential option is an FHA 203k loan - you would have to find out max fha loan amount for your area, but that program allows you to put down 3.5% of your acquisition cost - you need to find a cool local guy to talk to who you can ask about all of this stuff, ask all of your friends, etc for someone you can call and just talk to normally who isn't a stuffy banker type
GL - burns