Zamar,
I've had pretty good luck with a local mortgage broker in the area where I buy. They get me mortgage, private financing, etc, on short notice when I need something in a hurry. When it's not a rush, I give them as much notice as possible. It seems to work out well. Starting from your position, I would call a couple brokers and ask if they can get financing in a hurry. One of them should say yes. Your timeframe of a few weeks should be fairly easy for a broker. For instance, mine got me a mortgage starting from a cold call in three weeks and a hard money loan in days.
Good luck,
Ray
Keep us all posted on how this works out for you.