This sounds like a great approach. I just ordered the Lancaster books, but I'm also putting together an order from Digikey. Is there a part number for the switched Butterworth LPF?

Just implemented the circuit. This is the coolest trick for generating sine waves I've ever seen, perfect for this application. THANK YOU!

 

The 555 configured as a monostable multivibrator receives input on pin 2 the trigger.
The pierce xtal oscillator can be used as a the trigger source. The pdf gives most of the specific information
that makes you proficient so with Lancaster you can cook up something. It is complimentary to what you are doing,
https://www.ti.com/lit/ds/symlink/lm555.pdf

 

I was assuming that he chose the 4049 because his supply voltage was >5V.
If not then the 74HCU04 would be a better choice. It theoretically should be the unbuffered HCU for the oscillator, not a HC, but I've managed to make Pierce oscillators out of all sorts of buffered gates, NANDs, NORs, EXORs.

Follow-up question: I replaced the CD4049UBE buffered inverter with a 74HCU04 unbuffered inverter for the Pierce oscillator. In both cases, I'm running at 4.8V. The 4049 gives clean waveforms. The '04 output resonates but it's clear there's some variance in the waveform with the same input setup which makes the output look fuzzy. I've experimented with different R/C combinations but nothing has made the output as nice as the 4049. If an unbuffered inverter in principle is a better choice, what steps do I need to take in order to get it to behave as nicely as the 4049?

 

A 4049UB is UnBuffered!
What's your supply voltage?
Generally, to get a good square wave out of the same IC as the oscillator, you use a few of the spare sections as buffers.
Only the section with the feedback around it needs to be unbuffered. If you put feedback around a buffered gate it tends to oscillate on its own, perhaps not at the frequency at which you want it to oscillate.