I'm having the same issue. I even purchased the device found in this topic to see if that would help.

https://pinside.com/pinball/forum/topic/announcing-new-product-to-help-resolve-resets-in-wpc-era-games

This device did prevent the machine from rebooting so your theory on the dragging of the voltage is probably right, but I have also tried hooking 5V from another source (4AA batteries) and the saw still won't run. If I just connect the saw direct to 5V it works great. But connecting via Tom's board it won't go.

I'm going to try the 1.4 ROM and the alternative connections found here: https://pinside.com/pinball/forum/topic/diy-tom-tiger-saw-mod-for-14h-rom-based-on-the-former-pin-logic-kit. At least Tom's kit came with all the motor hook-ups but the board and work around seem to be a bust for my machine.

Hopefully our notes on this topic will help the next guy.

The Kahr board and the homemade kit found at https://pinside.com/pinball/forum/topic/diy-tom-tiger-saw-mod-for-14h-rom-based-on-the-former-pin-logic-kit worked for me. Without the Kahr board mine would reset every time.