What can cause a lab DC power supply to become an AC power supply

Most of the power supplies that I have looked at have used some combination of analog and digital isolation, depending on the supply. Most of this is drawn from repairing a couple of HP/Agilent/Keysight E3600 series power supplies. Generally, there are at least two processors: one is an I/O processor for the GPIB/serial interface, and a different one manages the user interface and direct control over at least one power supply channel. These two generally communicate via a pair of optoisolators. The I/O controller shares a ground with the I/O connectors on the back. The main controller is grounded to the common of one of the power supplies. In supplies with more than one output, the other output is connected with analog optoisolators to the main supply. I think there was something like 6 optoisolators connecting the two channels together in my E3649A dual outut supply, some for analog signals and some for digital signals. I have a triple output Tektronix supply as well, but I can't remember how it's wired offhand. With optoisolators, I think they do a good job of passing an analog signal through if they are driven in current mode, so you will need op amps on both sides to condition the signal.

MCUs are very cheap these days; it may be advisable to put an entire microcontroller on each channel and then use some sort of serial protocol for communication through digital isolators. The Atmel XMEGA series has built-in DACs and ADCs and lots of serial ports (4+), for example. One of these per channel and one more for a main controller could be a very nice design, and it would only require two digital isolators per channel.

When decoupling the use of parallel capacitors with values that are decade apart is like playing russian roulette. That is because you will get a resonant spike when the network with the bigger capacitor has become inductive and the network with smaller capacitor is still capacitive. I don't know if this is the problem here but maybe you should try replacing all the capacitors with one value either 10 or 100n. I did fast ltspice simulation to illustrate my point. This is impedance with two different value capacitors connected by traces with identical inductances.

And this is impedance with identical capacitor values.

Edit: Here is the simulation file as requested in comments:

Version 4 SHEET 1 880 680 WIRE 208 208 -16 208 WIRE 304 208 208 208 WIRE 208 240 208 208 WIRE 304 240 304 208 WIRE -16 336 -16 208 WIRE 208 336 208 304 WIRE 304 336 304 304 WIRE -16 480 -16 416 WIRE 16 480 -16 480 WIRE 208 480 208 416 WIRE 208 480 16 480 WIRE 304 480 304 416 WIRE 304 480 208 480 WIRE 16 544 16 480 FLAG 16 544 0 SYMBOL voltage -16 320 R0 SYMATTR InstName V1 SYMATTR Value "" SYMATTR Value2 AC 1 0 SYMBOL cap 192 240 R0 SYMATTR InstName C1 SYMATTR Value 100n SYMBOL ind 192 320 R0 SYMATTR InstName L1 SYMATTR Value 3.5n SYMBOL cap 288 240 R0 SYMATTR InstName C2 SYMATTR Value 10n SYMBOL ind 288 320 R0 SYMATTR InstName L2 SYMATTR Value 3.5n TEXT 432 256 Left 2 !.ac dec 1000 1 1000000000

The expression to plot is:V(n001)/I(V1).

Also I might not have understood correctly how you connected the capacitors but since inductance has a big influence here you should make sure that all the parallel caps are not connected through common but separate inductances. The motivation is that when connected in parallel the combined impedance of capacitance increases while the combined impedance of inductance reduces. So multiple capacitors having current flow through the same via is bad idea for decoupling purposes. Do whatever you can to avoid that.