I have a need for a high-performance string hashing function in python that produces integers with at least 34 bits of output (64 bits would make sense, but
"strings": I'm presuming you wish to hash Python 2.x str objects and/or Python3.x bytes and/or bytearray objects.
str
bytes
bytearray
This may violate your first constraint, but: consider using something like
(zlib.adler32(strg, perturber) << N) ^ hash(strg)
to get a (32+N)-bit hash.