I got up and running on an ATTiny85 - but not on ATTiny13. Seems that i2c is not supported. Have to find a 24 or something with USI support

For the '85 - I added a small delay to the beginning of initialise to allow the power to stablilise to the display (not sure if it's actually needed)
I clocked the MCU at 16MHz (internal - this isn't an option in FC but set the fuses from Arduino IDE). I notice the clock options in build properties are a bit odd (lots of ATTiny15 options?)
I also shrank the charset lookup and PrintChar displays lower case characters as upper case (not sure if this is really needed).
Have a PIC16LF15313 with 3.5KB flash and 256bytes of RAM - will give it a whirl too

Will also try and find one of the larger (64 pixel height) displays to test.
Martin