I didn't get the question until now. By auto-correlation you mean a sliding correlation so that each result is with a different delta in time. No, I think that has comparable computation to a DFT and the advantage of the DFT is that it can be done over a subset of the full frequency range rather than always having to calculate the full range like an FFT.
However, to find the frequency of interest a broader auto-corr or xFT would need to be performed initially. Then a detailed analysis could be done to hone in on the exact frequency.
I'm also intrigued by some of the "stroboscopic" methods, but I haven't looked at how to implement them yet.
My current thinking is that no matter what method I go with, it needs to be very high "performance", meaning highly accurate and reasonably fast. I believe the market is not large for this particular device. So better to go Cadillac and charge a price premium than to try to find a spot in a crowded, high volume market.
So that means, will an auto-corr approach do a good job of resolving a fraction of a cent for a tuner in less than say the two or three seconds a note will sustain? I would have to consider just how accurate the auto-corr might be.
Rick