Chances of getting a collision is higher than getting a good solution, but having multiple hashes does help in increasing the chance at a good solution. With a hash 1 bit less than the length of the file, we put two pigeons inside one hole, and have a 50% chance at picking the right pigeon. The fewer/smaller hashes, the more we get "sorry, but no".
It's easier to just drop the final F bits from the N-bit input stream and, at decompression time, guess what they are than to go through this exercise of generating hashes that have N-F bits in total and hunt for bit streams having those hashes.
Also, I guess the hash algorithm could be specifically tested to work for this particular solution, couldn't it (although only after having spent the $100 of course)?. The problem I guess is to have a script that takes up less space than for the hash to still work without a collision for the particular data. Even with the smallest possible program or script, this probably isn't going to work then.
