Thanks to some tips from you guys, the heating element replacement was completed without incident. Unfortunately, that did not resolve my issue. I am happy to report, however, that my dishes are now coming out dry and sanitized due to further troubleshooting, and I wanted to offer a PSA for how I did it because nothing I found through googling was ever gonna point me in the right direction. In fact, it was this comment from Dave. which got me started down the right path.

He was absolutely right. There should be some sort of protective device, not only to protect the element, but to protect against fire. So I started over and dragged the dishwasher back out, but this time I tipped it into its side to get to the underside and looked around. I followed some wires to a little switch mounted to the underside and there was a little black button on it. I pressed it. click

That’s. All. I. Had. To. Do.

It’s a little thermal cutoff switch. I just had to reset it. If anybody has a problem like mine, try this. But just know that it tripped open for a reason, so figure out why. In my experience, it was from my wife not knowing that “I’m flushing the water heater” doesn’t just mean “no access to a hot shower”; it means “don’t run appliances that are connected to hot water lines” lol.

Thanks again, Dave. I’m happy to have solved another problem!