Does changing the Resistor from button debouncing reference design require a cap change?
I would put a scope on the various nodes in the different circuit configurations to see what is really going on, but here is some speculation on my part.

I think you sized the cap suitably for the resistor change in the case where the switch is opening.  That is confirmed by your simulations.  When the switch opens (assuming it starts closed in steady-state), the cap will charge through R194 and you get the typical voltage decay you would expect.  The timing is about the same with 220k + 0.1uF as for 5.1k + 4.7uF.  I don't think the debounce issues are appearing when the switch opens.

When the switch closes however, the larger cap is being shorted by the switch, with only the 100 Ohm resistor, and its own ESR to restrict current flow.  Take a look at the 'current' through cap (the moving dots) when the switch closes in both simulations.  There is no noticeable current in the case of the 0.1uF cap, but there is some with the larger cap.  This additional ~20X energy stored in the cap to discharge through the switch.  I'm not too sure about the mechanism causing bouncing - the voltage and peak current are not higher, just the period of time is extended, but this might be exacerbating the bouncing.

So I think you would want to try changing the 100 Ohm resistor.  To keep the discharge time low, you would want to decrease that resistor to 5 Ohm (or remove it altogether), but that would lead to higher current through the switch, maybe even too much for the switch to handle.  You could try going the other way with a higher value but that would extend the discharge time and decrease the current.  Based on your results I think a lower value resistor would work better, but again may not be suitable for the switch.

Another thought is that the 0.1uF cap is going to have a higher cut-off frequency than the 4.7uF cap.  So the higher value cap will behave more like a short circuit at lower frequencies than the 0.1uF cap.  Each bounce will produce a burst of frequencies, and perhaps the lower value cap is being counterproductive because of its frequency response.

All that being said, give your observations I would probably just leave the 0.1uF cap in with the 5.1k resistor.