A missing inrush limiter will not be causing the reset problem -- but a bad inrush limiter can cause the problem. Completely removing the inrush limiter eliminated the inrush limiter being the cause of the resets. Not a bad idea to put one back in. Williams used quite large caps on some of the supplies. The current inrush at initial turn on to charge the caps is pretty high - the inrush limiter cuts down a little bit on the initial current spikes.
Before moving to BR's and caps -- look at the cheaper and failure prone connectors first. Just a few mate/unmate cycles can drastically reduce the effectivity of the internal connector contacts.

Some WPC power boxes don't have them.

They are not absolutely necessary, although it's easy enough to wire one in.

That being said, I had a cracked solder joint on one of the hot wire segments that was causing resets on one of my games.

Check all of the connections now that you have the box open, including the tension on those QD connectors.

There are a lot of joints in there that can go flaky.

RussMyers

Wow, I didn't even know Pins used thermistors Interesting...