If the items were the same, as well as the items per set, and numbers of sets, then that's good. But, I don't know what you mean when you say "I generated 3 different designs for these studies". It probably means you had three separate studies, and used the default settings which would generate 300 "versions" per study. Each study probably used the same starting seed? So, in reality these studies all used the same 300 designs?
Now, if you just used a single version (block) of the design for each unique group of respondents, this would be a bad thing, as you would confound pychological order/position effects with true differences in utility between groups. But, I doubt this is what you did.
So, assuming you used lots of different versions (e.g. dozens or hundreds), even if they were generated using different design seeds, just combine them all within one .CHO and submit to latent class software. No harm done.