Hi again, Eight,
On simulating your circuit and looking for solutions, I found the principal issue was: connecting the op amp V+ power pin to the voltage reference output, when I connected it to Vin, the horrible non-zero Vout signal went away, that applies with or without Cdelay in-circuit - the issue seems to stem from which node the OA is powered from (in the simulations I just did, at least). Not sure what you would do if it is vital that the OA output not exceed 2.048V, besides e.g. clamping the output one way or another to ~2V...
I simulated with both the LMC6464A and with the OPA322 as the OPA365 is not in the models in the simulation tool, I'm sure you'll appreciate the time it takes to locate and build models, and I suspect OPA365 and OPA322 are very similar parts (OPA322 gives a much cleaner/tidier Vout signal than the LMC6464, btw).
Cdelay as 100nF was equally valid as the 1uF in the schematic because Vthr had reached its 1.024V level by the time Vin also reached 1.024V, so Cdelay value is a matter of choice/requirements, presumably whatever minimum amount of time it takes for Vref and Vthr to get to where they need to before the Vin signal reaches the OA.
Let's ignore AM VS1 as the 330mA spike is due to the 10R*1,000uF inrush current at power-up. I removed the 2M R5 hysteresis resistor for no other reason than just because I wanted to, it works the same with or without it (with minor differences, obviously).