Timing between words in SPI
I haven't used the dsPIC DMA engine yet, but this sounds surprising to me.  When you say "continuously writing", does that mean in a loop waiting for the SPIxIF flag (or whatever it's called, not looking it up now)?  I expect that's the same flag that is used to signal the DMA engine to transfer the next word.

If you're not waiting for SPIxIF, then you're just jamming data into the SPI buffer and the output bits aren't predictable.  Perhaps there is a inherent gap between words.  What is the SPI clock rate in terms of instruction cycles per clock?

SPI is inherently synchronous, so a small gap shouldn't cause problems.  Unless you're trying to use the SPI peripheral for other than SPI, your requirement doesn't make sense.