Solid State Relay/High Voltage Switch unacceptable transient behavior
We went ahead with a test board to verify if the Vishay SSRs (Vishay VOR1142B4) would work for our application. The short answer is yes, they do. These do not show any of the problems of the IXYS CPC7524 which suggests that the problem with those switches is the protection circuitry removing the bias during relatively slow transient conditions.
As can be seen in the following figure, without a load, both sides of the switch are undistinguishable from each other (the two traces are on top of each other), which was not the case with the previous switches.

The following is a figure that shows a similar test condition as indicated in the question above (only the critical traces shown, as other tests confirm the 400pF parasitic capacitance on the nodes and the traces across the switch are nearly indistinguishable from each other with a quite consistent and constant 22Ω series resistance).

Note that the voltage at CH1 reaches the feedback condition almost instantaneously on turn-on with no chatter or other issues, however other circuit imperfections mostly due to parasitic capacitances across M1 have now come to light.
This comes to confirm that old adage of &quot;simpler is better.&quot;