Secure content-defined chunking
UMAC uses AES, so it will not lead to a faster algorithm than the rolling hash + AES solution suggested in the previous question. Universal hashing based MACs like UMAC and Poly1305 usually use a PRF (which you could just use directly) to hide the hash. There are universal hashing MACs that do not, but as far as I know they are even slower. (Further, I am not sure if a secure MAC would even be enough, or if you actually need a PRF.)

Without leaking any more information, there are not many options. Rolling hash + SipHash is probably faster anywhere that you lack AES hardware, but that may be the best you can do.

If you find the performance cost to be unacceptable, you might want to allow some information to leak. For example, if you define chunking using parity(w) = 0 and then PRF(k, f(w)) mod (n / 2) = 0, you halve the number of PRF calls while only leaking one extra bit of information on the window (and even less for those positions where you did not end a chunk).

You can of course reveal even more information to reduce the number of calls further, but in the end you back at something leaks as much as just using f(w) mod n = 0.