Well there's your problem...
Add probably 10 to 100 milliohms in series with one or more caps and you'll probably have it solved. Ya, I know... the solution is worse than the problem
Can also try improving the pole-zero or lead-lag compensation on the error amplifier (probably going back to the TL494 error amps, look for a voltage divider from one or more outputs back to the TL494 input(s)), but the root problem is a voltage mode forward converter has a complex double pole in the loop response, and wrapping a control loop around that usually makes either a uselessly slow loop (an integrator with large response time, so the output over/undershoot is massive) or an oscillator (which is the case here).
Capacitor ESR is beneficial because it puts a zero in the control loop. If it happens to be on top of the controller pole, or near the complex poles, that gives the loop a boost in phase margin, keeping it stable.
I suppose aging of the filter choke(s) is a possibility, too. Let me guess, the core is yellow on three sides, white on the other? Those things are almost better as resistors than inductors... but again, loss is kind of a helper on this topology. Except that the internal heating leads to breakdown in the core, which makes it hotter and so on. If it looks like it's cooking, better to replace it (at which point, you might as well replace the whole power supply, eh?).
Tim