Ok, so you've started with the full model and that's perhaps causing you problems, let's start with just the two elements that we need to think about self-discharge, capacitance, and leakage resistance.
In this simulation, I've just put a capacitor, value of 22u (looking at your data that's the correct value of 22e6 pf), and 4M Ohm leakage resistance. I've set the inital voltage accrosss the capacitor to be 120V, and you can see in red the voltage, and in green the current out of the capacitor, both decay exponentially as expected.
So why the exponential. Well at the start, the capacitor has 120V, and it's discharging this into a 4M resistor, so as you'd expect
I = 120/4e6 = 30uA
and that's where the curve starts. However, as the capacitor discharges, its voltage drops, therefore the current drops, and therefore the rate of discharge also drops, and this creates an exponential relationship.
Because the rate of discharge is decreasing over time, the relationship is no longer linear, but exponential.
You might notice that above the time is very long, 500s on the graph. Roughly speaking, a capacitor takes 5RC seconds to discharge, and in this case that would be 439 seconds. If I now add the rest of the lumped elements in the curves look like this
At first glace it looks like the current is zero, but actually this is becuase of the scale. The initial current in is so high (>100A) that our discharge at 30uA is impossible to see. I have to do a bit of fussing to be able to see it.
In this case, I have to start the simulation at 5us, after the charging pulse, and constrain the axis a bit to get it in veiw. Without this delayed start, my simulator gives me a warning and shows some weird stuff.
Swapping back to your settings, 22pF for the capacitor and 30uS simulation time, I get these results.
Which is what I'd expect, some spikes around the switching event, but then a nice exponential discharge. You might think those discharges were linear, untill you look at then on a longer timebase, hence why calculating 5RC was important.