This is no hardly working WMS crap dragged along from the Seventies, Spike is a well designed system.
When do these resets occur? Is there a pattern behind them (certain action in the game)? Can it be provoked by quickly hammering both flipper buttons at once? Maybe try reseating the power connectors for good measure (although the onboard caps should be able to buffer that up).
If your PSU is faulty (or the big filter caps are bad), you should be able to notice it by turning off the game while sound is playing and seeing if it stops immediately. If is runs for a few more seconds, then imo it should be fine.
The CPU reset pin is not tied to a reset IC that might cause trouble, just a pullup and a button, as long as the soldering is fine there shouldn't be any trouble. The main voltage converter on the cpu node operates down to 8V, so until that fails, your coils will have lost power long before.. Unless it's a mechanical defect (broken solder joint) or a defective component on the cpu board, I find a hardware issue highly unlikely.
I'd rather suspect a software issued reset, and that might be caused by a bitchy SD card. Before swapping the PSU I'd just write a new one (https://sternpinball.com/support/sd-cards/). If it works, nice, if not, use the card for your camera/phone.
From the looks the PSU in my game is the same (although with a bug 230V sticker on top), and the fan is definitely always running - I've never heard it speed up further though..