Serial or even Parallel eeprom is definitely slowww. SRAM is definitely the way to do this. The modem transfer part is bound to be intermittent and anything short of buffering the entire image before sending will cause trouble. One moment I was hoping I could suggest a MiniSD card storage; however, that too is flash memory and is slow.

If you can start and stop the camera data transfer via some protocol on your PIC device, maybe like a simple xon/xoff handshake too might help to slow down the camera side transfer to what your PIC can manage and then stream out the data on the fly.