Hi Rick,
I think you should be able to map an ISR to the NMI at runtime using the SYS/BIOS API Hwi_plug(). The Hwi_create() API won't let you do it, as it only allows creation of maskable interrupts, whose interrupt numbers are less than 15.
Based on spru430e.pdf, Table 3-1, it looks like the interrupt number for NMI on C28x should be 18.
Can you try calling Hwi_plug() to map interrupt 18 to your own ISR? Hopefully your mapped ISR will run when the NMI occurs, then in your ISR, you can try doing your logging, etc.
Steve