@jonwa -- yes it should be possible. Just remove all the SPI references in the library. Do a diff between the code I have on github and the official LPD8806 library from adafruit and you should be able to replicate the differences in the library you want to hack.
Bitbanging is a way to serially communicate in software, as opposed to dedicated SPI hardware. This means that instead of using a hardware SPI (which the digispark doesn't have), we use output pins from the arduino to speak serially to the chips on the LED strip.