I2C only takes 2 wires and 2 external pullup resistors. The protocol can be handled by bit-banging in the code- many examples of this- and some PICs have an I2C hardware module. The hardware module certainly allows the code to run faster, but it is a rather poorly documented module (very atypical of Microchip to do this) and the hardware itself has a number of errata pertaining to many of its revisions.
Also don't forget there are other PICs with much more memory.
If I may ask, what kind of color display do you have there, and how are you driving it? I've long wanted to use a color display but the cost effective options are quite limited.