If a hash function is suitable for general use, it will be suitable for this use. So long as an attacker cannot find two binary strings that hash to the same value, your method is secure. If you aren't confident that's true of the hash algorithm you are using, you picked a bad algorithm.
Saying that an attacker has 32,768 opportunities to find a collision and therefore it's easier is invalid. He can just as easily try to find a collision for a single binary image by trying 32,768 different possible inputs at a time. There is no reason to expect some blocks to be stronger or weaker than others, so no reason to think more opportunities make it any easier. (Since he can replicate has single opportunity anyway.)