I have tested my Minima controller successfully for support of 16x2 or 20x4 LCD displays using a 5V i2c backpack. Here is a 20x4 display running my changes to WA0UWH's latest firmware for Minima.
Only two wires plus power and ground required to support these displays. The code is conditionally compiled with or without i2c display support as desired with the default to continue to support 6 wire displays. Converting to an i2c display will be required in order to free up I/O pins to support such things as rotary controllers, keyer paddles, etc. This change however will continue to work by default with the original Minima hardware configuration for the LCD display. In order to enable the functionality, please uncomment the following line near the top of the file "radiono.ino".
#define USE_I2C_LCD 1
You will also need to obtain the i2c library LiquidTWI and install in your Arduino environment in order to build with this support.
It should be noted that my Minima Controller shield is not required to support i2c displays.
Please contact me directly by email at ko7m at arrl.net or by commenting on this post if you have any problems and I will do my best to assist.