I remembered reading something about TTL xtal oscillators and problems with variable impedances, and, after some digging, found it.
The schematic attached is taken from "Crystal Oscillator Circuits" by Robert J. Matthys, Krieger Publishing Company, 1992. It is described in Sec. 11.3 "TTL Two-Inverters-7404", pp. 160ff. This kind of oscillators are described as "waveforms are fairly good" and "relatively insensitive to power supply and temperature" but "many versions of this oscillator are poorly designed".
The idea is: a single resistor feedback around the inverter is acceptable only in the second one, but not in the first. The reason is that a TTL gate has a gain of 10X, but because of feedback, the 470 Ohm resistance has a dynamic impedance of 470 Ohm at the extremes, but only 47 Ohm when transitioning. Such unequal load is not aceptable as a crystal load.
Hence the peculiar feedback around the first inverter. The resistor-capacitor tee is used to reflect the load RL to the crystal the whole oscillation cycle. This very much reduces distortion (and is recommended also for CMOS inverter oscillators). The shunt resistor R3 has two functions: pulling the inverter into the transition region, so both the input and the output of the inverter are somewhere near 1.6V. Second, to trim the duty cycle of the oscillator to a perfect 50/50 ratio.
Now the circuit given is designed for operation at 1Mhz, whit crystal resistance of 240 Ohm (therefore, RL = 220, a little less). At 32Khz, the load resistance should be around 20K, so RL should be set to that value or a little less. I have no TTL inverters at hand, nor the time to test this circuit, but maybe it can help. Anyway, my guess would be RL = 18K, R3=200K.