I have NEVER had this happen.
What is the exact number on the chips being used?
Also (though should mean nothing) I don't use any board to mount my ICs on. I keep my mods cheap because well, people are cheap and I can't get good money for mods. I solder both ICs together then glue them to the bottom of the board for the HuCARD port.
I use a simple two way switch like yours and very thin wire.
I use a third party 1000mA PSU.
I draw +5 voltage from the + end of the 10uF capacitor on the HuCARD port board (this part should mean nothing however.)
Every single PCE I've modded in this way is also modded for RGB with a full amp circuit. The amp is placed in between the ribbon cable. I don't use a board for that either!
I've modded like twenty of these for customers this year and not a single one has reported an issue.
Now occassionally I do get an interference issue on first screwing a unit together, this is solved by unscrewing, moving wires, moving the amp. I don't understand why these issues would be considered so common as to resort to that enormous switch. Might look OK on a Duo but it's not good on a Core. I see you put a hole in the Core for your IC mod switch, which is the sam place I've put it in the past. The only feasible place really for the 8PDT switch to go in a Core is behind the AV out with the switch sticking out the back (but not too far to plug in a CD ROM unit.) And all the consoles I've seen modded this way had had that config. Plus you can't use the existing hole for a switch in a white engine if you use the 8PDT. Nor can you engineer a switchless mod.
You know what I'm guessing this issue is? The more stuff you cram into a console the more likely you get interference. The less space in the unit, the more squashed it gets when you screw it together. So you keep the parts to a minimum. I don't use the prototyping board. I'd rather glue IC components to existing board then solder onto the legs of the ICs. Keep the wire thin and short. But not too short it can catch and be pulled undone on something.
Here's another issue. The Core Grafx has a metal plate in the casing above the port. I had modded 5 white engines using IC mod before I tried a Core and I short circuited the unit. I didn't take note of the metal plate. The blobs of solder you apply can end up touching that plate. If you bend back the pins in the HuCARD port to do the mod, they DEFINITELY will touch that plate. It won;t damage your console to plain remove the plate (apply heat to where it has been literally applied by melting the plastic casing, melt it off.) Or if you prefer, seeing as that plate is added to prevent interference you can simply cover the mod up with tape.
I think if you made your mod like mine, ie don't use prototyping board, use the same socket mount ICs I do, glue ICs under the HuCARD port, use thin wire, draw +5V from where that capacitor is soldered, you would not have power or interference issues. The only issues you would have would be related to wiring the mod wrong, which is easy enough to do and you'd notice it right away anyway.
Your other problem here is, you are modding a console that's been fixed before. And the crack you had was all around the power in port. You could have some damaged components there which are causing a loss of power and could be affecting this mod.