The problem is that the firmware with both new features and support for a graphic LCD module will exceed the flash size limit of the ATmega328. The classic HD44780 testers should be fine (for some time). Anyway, we're heading to the 644/1284 to allow new features and options. On my todo list is support for touchscreens which requires some additional I/O pins, the 328 doesn't have.
64
4/128
4 because of the 20MHz clock? - well done, it improves the felt speed with higher resolution displays on old-school-8bit-mcu's
the bad thing with them ist the restriction to TQFP-44.
BTW, the low capacitance measurement is very sensible to probe wires and ZIFs/test sockets. Karl-Heinz mentioned that the difference between an opened and closed ZIF is about 0.6pF and that probe wires are a no-go.
to solve this, I'd recommend to "duplicate" the circuitry for the three test pins, one set on ZIF, the other on wires.
most well designed self-made testers have already a ZIF (or other 3pin) socket AND probe wires on 2mm banana jacks.