What are some really accurate ways to get the value of a peak (local maximum) given some points around it? (To be used for autocorrelation peaks.)
Assuming the autocorrelation of a sufficiently long piece of sinusoidal signal has a good SNR (which it probably will), yes, that quadratic interpolation is quite good, as the sinc (which is actually the interpolating function) is locally quite close to the shape of 1-x². I've done similar things to estimate locations from signal crosscorrelations.
It gets problematic when the noise in your sines is high, or when you try to achieve a resolution much smaller than the sample distance (as the sinc gets quite &quot;flat&quot; when you zoom into it around 0 – and thus, the smallest bit of numerical error or noise leads to a large mistake).
Often, people are pretty happy after sinc-interpolating their signals, and it's not a very computationally hard thing to do:

Take your signal, as is
DFT it (using the FFT of signal length)
add plenty of zeros to the DFT's end (e.g. to pad it to the next larger power of 2, which increases the length by some factor $\alpha$ of your choie)
take the inverse DFT (using the IFFT)
Do your crosscorrelation, without interpolating

Tadah, $\alpha$-increased resolution.
This isn't great in terms of estimation variance (Fisher information didn't change, since the signal energy stays the same).
Since you know you're dealing with a dominant sine, a parametric spectral estimator would perform well. For a line spectrum ESPRIT is an appropriate choice, but autoregressive models lead to other good approaches like Yule-Walker, etc. If you're working in  a framework that can offer ESPRIT, I'd honestly try it.