I'm not sure I understood the question correctly, but I hope my answer is still helpful for you.
Further to that, if the number of sub hashes and vectors is increased to 10, by permuting each of the four sub hashes against the other 3 and XORing, does that substantially decrease the odds of false matches? (Or increase them? Or leave them the same?)
Statistically, the only thing that matters for the probability of collisions is the total entropy of the hash. If you create a 128bit hash over a string, you have 128 bits of entropy. If you create two 128bit hashes, one over the first part and one over the second part of the string, you have 256 bits of entropy. If you XOR the two hashes, and use the results, you have 128 bits again.
If you use one 128bit hash, the probabilities for getting no collision on inserting the nth number is
P(no_collision, n) = (1 - 1/2**128) ** n
I'm pretty sure that the number of collisions follows (at least approximately) a Poisson distribution, though I haven't yet figured out how to calculate the expectation value.