Take smaller bites of your data, and checksum those bites. Then see if you can see a pattern in at least some of those bites.

Say you take four byte cheksums at every byte, and the pattern is fourteen bytes long and repeats every 30 bytes. You start collecting at offset 0, 1, 2 .. and collect checksums for those spots. By the time you get to offset 30, you'll start to see the same checksums. Now, only three of these will match, but that positive result would be enough to backtrack to 0 and compare the stream byte by byte from there and from 30.