I did not expect to have issues programming any of the microcontrollers with a J-Link, but I certainly did. Apparently others have had issues programming these when running at 5V. At 5V, I was unable to program. At 3.3V, it programmed the first time.
I have no idea what's causing this, but I did notice that even when running at 5V, the J-Link reported 3.299V at VTref. That seems odd, considering the output of the regulator measures 5.02V.
My fear of the LED voltage drop not being sufficient at 5V is indeed correct. At 3.3V, the LEDs are either off, red, or green. At 5V, the LEDs are either mostly green with a hint of red, very green, or red.
The primary microcontroller on each board only has one pin I can use for LEDs, but since the others have the two lines that would be used for the second serial port available, I can use them to drive the LEDs separately. That would mean only the primary would have issues. Still, I'll probably rip off all of the green LEDs and just use the reds. It'll reduce the cost by $0.05 per board anyways.