The same "problem" occurred when people invented GPU mining, then FPGA mining, then ASIC mining. As long as SHA256 isn't broken, it doesn't matter what kind of speedup miners manage to get; whenever someone finds a big advantage, everyone else uses it soon enough.
> Different basis of hashes are obvious
"Use more hash functions" is sort of a reflexive response you get a lot from non-cryptographers, but the intuitive reason this is a bad idea is that if your hash function isn't broken, your cryptosystem shouldn't be either. It's better to fix the cryptosystem than to half-assedly patch it over by obfuscating any problems with more hash functions.
> but maybe some type of actual work every so often as well.
What do you mean by "actual work"? In all likelihood, whatever you're thinking of has none of the properties that make PoW a viable mechanism for sybil resistance.