So I sat down to test out the board I build, after removing the 3.3 V regulator, and discovered it was not responding to the debugger. To power it, I was using 3.3 V from the LaunchPad. The LED on my board lit up just fine but the TM4C's internal LDO regulator was not putting anything out on VDDC. I spent a few hours troubleshooting but came up dry. At this point I think powering up the regulator incorrectly caused an electrical problem in the microcontroller.

Next step: Using the third board, build up another circuit with just the bare essentials needed to operate the microcontroller and attempt to program it. If that works, it confirms that the basic support circuitry is correct in my design. If it does'nt work I'll redesign a barebones board to prove out the base design.