Wow, the arm_math CMSIS stuff is really nice. Tons of stuff there, and the source is available, and even optimized to use SIMD instructions when available.

I think I'm going to go with a vector dot product, and slide that down a smaller window based on where I think the opening waveform is. I don't have the memory or need for the full correlation waveform, just peak correlation detection, and I think I can use a smaller window around where the ADC WD tripped, then scan down the other channels looking for peaks in correlation where the start of the waveform matched.