Overcoming mortgage contingency

[Parnell C.]

First post but I've been lurking for a while. 

Quick run down, we bought our first home, a foreclosure and have it under contract for a nice profit. It closes 10/13. Found a second home to rehab which is also a forecloser. This home is under contract as well and closes 10/24. 

Now a large bank pre-qualified us for the second home while owning the first. Low and behold now there is a contingency for us to sell our house before we close on the new one. 

So this wouldn't be a problem but our contract states no contingencies (other than financing). 

How should we handle this with the seller? They obviously didn't want an contingencies but we can't avoid it. Would putting more money down help? This deal has been burtal but we see a ton of upside if we can make it work. And advice would be greatly appreciated!!!