Chris,
Fun problem :)
Looking ahead to when the timing works, you should insure you use -mi with your algorithm code when you turn on optimization, i.e., non-debug build.
The jitter in the ISR start time does not seem too far off from what might be expected. If I interpret the trace correctly (nice - thanks for providing), the ISR jitter is 350ns (960 - 610). Not sure of your C6748 clock speed, but this would be <150 clock cycles, which could be accounted for by kernel latencies or other disabling of interrupts in the system.
I'm not really familiar with the McBSP peripheral (other than I know it has lots of different operating modes) nor with the McBSP driver in the PSP you are using, so I have no suggestions for the ~7us jitter in the "issue()" function time. I took a quick look at the source code for the "issue()" method for McBSP - which comes down to the mcbspSubmitReq() function in Mcbsp.c. I don't see anything obvious related to kernel usage. Not sure about the McBSP or EDMA operations, though.
You may need to find a McBSP and/or EDMA expert for this.
Mark