Frankly, I wasn't aware of the 75-move rule! This indeed caps the length of possible games.

The threefold repetition rule doesn't have an equivalent (there's no, say, "fivefold repetition" draw that could be enforced despite the players' will), but it's really irrelevant from the perspective of solving chess, because there's no point in analyzing what happens if game goes through the same loop 1, 10 or 100 times.

And the 75-move rule sets a hard limit anyway, so you couldn't loop infinitely, even if it mattered.