I might not be able to find an LCD with a 24 bit parallel interface, which is what my controller requires. I have seen 18 bit parallel interfaces, though. I assume that I could really just use the lower 6 bits of each color and not use the other two bits per color channel. All I would have to do is make sure that my color palettes are adjusted accordingly, right?
You can do this without issue.
However, you want to use the Upper (e.g. MSBs) of the digital output, discard the least significant bits. Otherwise, you will get all sorts of interesting effects.
I currently have a similar project, which uses a 16 bit graphics controller, with a 18 bit LCD. In this case, you connect the 16 bit interface to the MSBs of the LCD, and ground the additional LSBs. What you are proposing is simply the inverse.
Note: I've always thought of the MSBs as being "Upper" - This may simply be a terminology disconnect. Anyways, MSB and LSB are a far better way to describe the bus.
have you looked at the PSP screen? it's 24bit parallel.