After two weeks with a bricked computer, I finally figured out to get it up and running without losing (almost) any data. In case anyone else finds it useful, here's what I did:
1. Using a USB 4.0 cable, I attached my 16" M1 Max MacBook Pro (bricked) to a functional M2 MacBook Air 13" running macOS 14.0 Sonoma (this did not work until I upgraded to Sonoma). For some reason the cable needs to be plugged into the leftmost port on the left side of both machines.
2. Opened Apple Configurator on MBA. Booted bricked machine into DFU mode by holding power, right shift, left option, and left control combo for 10 seconds (took several tries to get the timing perfect).
3. On the MBA, right-clicked my machine and chose Advanced > Revive.
4. Waited for the Revive process to finish, bricked machine booted up, showed my username. Asked me to type in my password. I did that, it blacked out and rebooted.
5. After the reboot, it asked me to log in again. Did that, it gave me two options: On the left, the name of my drive, on the right "Options". Clicked "Options".
6. Got the option to install Sonoma. Tried, but not enough disk space available.
7. Quit Sonoma Installer and opened Terminal. Navigated to my Downloads folder and deleted it, which gave me enough space to install Sonoma.
8. Quit Terminal and opened Sonoma installer, ran that, finally got in.
Prior to this, I tried reviving the machine several times to no avail. Clicking "Options" (as in step 5 above) only caused the machine to reboot, show the Apple logo, and black out. I tried reviving using ipsw files for 13.4, 13.5, 13.6, and 14.0 via Apple Configurator, but nothing worked until I upgraded the M2 MacBook Air to Sonoma.
Hope someone finds this useful, and I hope Apple vets their updates more thoroughly so they don't waste so much of their users' time. The number of hours I lost taking the laptop in to the Apple Store, buying a new laptop to use for pressing work projects for two weeks, returning that laptop, and attempting to revive the bricked machine is ridiculous.