A fast non-cryptographic hash function that is "strong enough"?
So what you need is a fast cryptgraphically secure hash function?
There are some.
If you're in hardware Keccak might be an option as it uses many bit-permutations.

If you're in software there are Skein and Blake2b/s/bp/sp. Skein was the fastest hash-function of the SHA-3 competition and Blake2 is the successor to BLAKE, the second fastest hash-function in the SHA-3 competition.

You might find this page helpful.