LCD1602 with AtMega2560

2 and 3 appear to be interrupt 0 and interrupt 1

They are, but, unless you are attaching something to them that can generate an interrupt AND registering a handler, using the pins is no problem.

11 and 12 are MOS1 and MIS0

Correct on a UNO or other 328 based board, but not on a Mega, and only if you use SPI.

The order of the pins that didn't work and the the order of the pins that do work is not the same. I wonder if that has anything to do with the failure to print with the first set of pins.