Many times I've got to gun and run with my HDR. I use auto bracket and most cases 3 shots at +/- 2 stops works fine. For my hand-held HDR, I set the FPS (motor drive in older terms) to it's fastest, usually from 5-8 fps, and either process the HDR in ACR or open the processed stacked as layers, align the layers then blend the HDR frames into the final image.
It does a reasonable good job overall, especially if there is some kind of movement, light when I have to shoot a portrait or small group under dreadful lighting/contrast situations, sometimes with dappled lighting.
Don't be afraid to crank up the ISO to get additional shutter speed. The slight loss of DR vs. having motion stopped in your situation for a better HDR stack is more than outweighed, IMO. IQ at higher ISO speeds with most cameras manufactured in the past few years is simply phenomenal I've found.