OK, if I understand correctly, you're using a timer to generate the DMARQ to clock the GPIO writes, but you also need timing to kick off the burst.
For 40us burst interval, could you construct a 50us buffer that contains the 10us burst + 40us of silence, and run the DMA continuously in circular mode?
For 2sec burst interval, could you construct a 1ms buffer that has 990us of silence + the 10us burst at the end, run the DMA continuously in circular mode, then use the DMA wrap interrupt to refresh the end of the buffer with either the burst or silence depending whether there's another upcoming burst?