So after 12 hours of imaging, errors, new imaging, more errors, I've come to some conclusions:

Native Ubuntu desktop (at least 18.04.4) just isn't ready for the Pi 4. A clean install got Ubuntu desktop (Gnome) working, but there are large gaps in wifi and bluetooth controllers. Despite finding some fixes that would get some basic functionality temporarily, it's clear that it's not talking correctly to the Broadcom firmware. I was still on "critical" firmware (VL805: 000137ad, BL: 2019-09-10) at this point, but I was frustrated enough that I wasn't interested in playing anymore. I think I ended up with four different installs trying to get this going.

After running into all the firmware issues, I decided to head back to Raspbian (Buster). It's a Debian OS so it keeps me close to my preferred Ubuntu, and it obviously has all the hardware support tested and baked in. I also opted to switch firmware channels to "stable" and updated (VL805: 000137ad, BL: 2020-01-17).

I knew ROS could be compiled from code, but my compiler experience isn't terribly robust. Ultimately, I settled on this guide and decided to give it a go. I skipped the section for the assimp fix as I didn't see any related issues in the build. On a Pi 4, ROS took close to 90 minutes to compile. Painful, but the results are worth it. I am currently up and running with ROS on Raspbian with no issues thus far. Stuck on Python 2.7.16 for the moment, but that's another challenge for another day.

Sidenote: I don't remember running into firmware issues with Ubuntu 19.10, but after seeing ROS wasn't natively supporting it, I wasn't in it long. It could be worth exploring again based on the results of the compiler.