ok, ok, putting noise through the narrowband passband was NOT a good idea for making a 'clean' oscillator source.
So use the fact that there's a lot of 'logic' potential inside a chip, but external connections cost a fortune...what's wrong with a set of two variable, switchable current sources? One source, one sink to GND driving the RLC node? The idea is to start out with very small current ramp up until reach voltage near rail, switch OFF and turn on he other current source, and head back down, near GND [or neg rail] reverse etc. Now increase the current and keep doing until the voltage turns around on its own BEFORE it reaches the voltage switch points. Make up an appropriate rule.
maybe reverse process starrt at high current and come down in current. But with enough stuff inside the chip, and coming up with appropriate rules, you should be able to make a nice clean, stable output based upon looking like a Function Generator output that is a bit independentof the Q of the external tank.