Or slightly randomly modify all the parameters on the copy you distribute, then it will be a match for nobody.

OK, this is a fun game. I think your counterattack assumes I'm picking these million weights uniformly randomly among the 175 billion. I modify my original answer: s/a million/half the weights in a deterministic subset of 2 million weights/

Select the deterministic subset by just hashing some identifier for each weight.

For any reasonable number of copies, there's a pretty unique subset between all your copies sharing a large amount of bits flipped in the same direction among this subset.