Has there been any science about say, mating some of the 13 year brood with the 17 year brood
I haven't checked when those are next expected (once every 221 years?). But at the moment it's the 17 year & 19 year.

Anyway, mating 'some' with 'some' might get progeny with a different periodicity, but you would still get the same major broods coming from the rest, just with possible complications from the extra brood you've created.