Hmmm, a Korg Trident has a LOT of guts, it's regulators will get pretty toasty. I've never worked on one but the photo of a TridentII shows a big PSU heatsink on the back, that alone is rare for a synth. Does your schematic have any markings for PSU testpoints and voltages indicated etc?
You can solder some 0.1 ohm resistors across the fuesholders, and remove the fuses. Then power it up and measure the voltage across the 0.1 ohm resistors, it will tell you how much current each part of the downstream circuit draws, so you can see if there is an overcurrent fault on any supply line. Old school techs have blown fuses with resistors soldered onto them , that they use for tests like that.
Korgs normally use sockets for all the ICs. I would draw a layout diagram, then unsocket all the IC's and place them carefully on the diagram in their respective place. Check IC's for miscoloured legs that might indicate it has suffered an over current fault.
Then power it up again and check for overcurrent on the 0.1 ohm resistors to see if you have removed the fault. There may be other regulators like zeners etc in the circuit, zeners tend to fail as a short circuit and drag PSU rails down.
With the 4558's I would be temped just to buy a bag and replace them all they would be under $1 each, with the more specialised ICs like the VCFs you can plug them back in and see if the overcurrent fault returns, which will indicate if an IC is bad. A shorted IC that is causing overheating of your voltage regulators will probably show signs of heat damage on it or around its socket etc.
I don't see any problem with disconnecting the 15v supply to different parts of the circuit to see if one part is faulty, juts be carefula nd write good notes of what you do and where everything goes. That is a complex synth packed full of PCBs full of ICs... It's likely to take a while.