How would one design a (quasi) linear phase adaptive notch filter for a single complex tone? While IIR notch filters are attractive, I need to retain phase linearity at the filter output.  I imagine that it's possible to use a standard IIR notch  filter:
https://www.researchgate.net/publication/224174145_A_Complex_Adaptive_Notch_Filter
followed by some form of phase equalization.
An alternative would be an FIR filter with conjugate symmetric coefficients.  I am unaware of any FIR designs in the literature explicitly for a single complex tone.

Any thoughts on the best way forward?
I might consider doing a complex modulation of the frequency you want to notch down (or up) to 0 Hz.  Then run your favorite deep DC blocker (plus phase adjustment if needed).  Then complex remodulate the result back to the original unshifted spectrum.

DC block: For non real-time, just subtract the entire signal’s average.  Or a long (weighted?) moving average if you can tolerate the latency (Rick Lyons has some notes on this technique).