I could be wrong here but i do not think you can read data from the display with a serial interface. I know in reading the data sheet it does seem to say there is a serial read possible but I do not see in the information how that could happen.
With the parallel interface you have an R/W data line to set for data read but with the serial you either have an SDC line for Data/Command with the 4 wire or an extra bit send with the 3 wire SPI but I can not find a provision for a R/W bit for a read command by data bit or by hard wire.
I am using a 16 bit parallel interface and it works excellent. Quick screen writes, easy to read data back, really no problems working with the display. You may want to look at changing your design if you can to a parallel interface.
Possibly a CFtech or other forum member can correct or confirm what I have said.
That's what I meant by it seems to say you can do an SPI read but does not seem to show how and there does not seem to be a way to send a 'read' command using the SPI interface. If you are trying to read but it erases the pixel data when you do that then it sounds like it is over writing the pixel data instead of reading it.
Try emailing Crystalfontz support and they should be able to tell you. I just don't see the info on how to do an SPI read in the data sheet although as you mentioned it seems to indicate it is possible on the chart you referenced. Do you see anywhere it indicates how you send an R/W read bit using SPI?