I did some more troubleshooting today and I have to admit that I'm a little embarrassed. I took the power supply and harness out of the cabinet so I could work on it on my bench.
I hooked it up to power and there was nothing. I then looked at the schematic and realized that I had to "close" both the safety switch and the power switch. Once I did this, I had the correct voltages on the transformers. So I went out to my cabinet and looked at the safety switch. Sure enough, it was in the "off" position. I didn't know that this cocktail table's safety switch works just like the stand-up cabinet. I pulled the lever out and did a continuity check on it and it was fine.
I was testing voltages with the safety switch turned off the whole time. So, it wasn't the filter.
To make things worse, I made a rookie mistake and actually cut wires on my harness to get it out, thinking that I'd reuse the molex connectors for the player 1 and 2 consoles as well as the coin door and monitor cables. I spent two and a half hours soldering the harness wires back together again.
With the power supply assembly on my bench, I tested the voltages across the fuses. They were terrible. As you can see based on the image, there's a good reason for that. So, I ordered two 4-position fuse blocks from Amazon. As soon as they get here, I'll reconnect everything and try again.
I took the opportunity to clean everything up and wipe down the wires. This cabinet spent many years in smoky bars and there was a layer of grime on the harness. It was so bad that I couldn't tell the colors of some of the wires.