What you describe is essentially what I was originally targeting, but buying a separate power supply module for each channel would add up quickly. What piqued my interest here is the idea of having one off-the-shelf main supply (perhaps even an ATX supply) and low-voltage, low-cost isolators for each channel. You might be right about forward vs flyback, again I have no idea what I'm doing and that includes choosing a suitable topology.
The way I envision it (and here I go, overdesigning already) each channel card would have two transformers. One main with a variable output that tracks the output voltage. And one housekeeping supply to power the digital bits. Perhaps +/-5V with post-regulators so it could also provide a negative supply to the opamps. The digital portion would include an inexpensive microcontroller to act as a DAC for the voltage and current set points (as discussed in this thread), and to monitor all the unregulated converter outputs where a built-in 8 or 10 bit ADC is adequate. For precise voltage and current monitoring you could either use a popular discrete ADC or something like INA226 that can monitor a current shunt and voltage directly and very precisely, with a I2C interface. The microcontroller would then interface with the master over isolated SPI so it can easily select each channel card.
There are few interesting variations here in terms of where the parts go. For example, the housekeeping converters of all the channel cards might be clocked from a single bus by the master, since they all operate with the same voltage and current loads. The channel card microcontroller might drive its own main supply converter through the isolation barrier, one benefit of having a separate housekeeping supply. It might be a bad idea though, depends on how well inexpensive high-speed digital isolators perform in terms of jitter etc. Worst case the master micro can drive it but it wouldn't be as responsive because it would be receiving feedback through the serial interface.
Another variant is to eliminate the channel card microcontroller, use an I2C isolator to bring out the INA226 measurements, and drive both converters and the PWM DAC from the master. But you lose the housekeeping measurements and you have to deal with giving the INA226s unique addresses since they'd be on the same bus and couldn't negotiate an address automatically. Plus, as discussed here already, micromanaging one PWM channel is difficult enough. Doing it for 4 channels while also working the user interface or even Ethernet is stretching things a lot although a Cortex-M3 could probably pull it off.
So yeah, there's some wild speculation for you. Hopefully you fine folks can refine and focus it a bit.