Q.sand cherry pruning
I cut my four, sad, old sand cherries down to about 8 inches. Some of the shoots are coming from the cut off trunks. Some are coming out of the ground around the plants. Should I select some to prune? Which ones? Should I trust the roots? Or dig them out and start anew?

You could propagate the root cutting. I would allow it to come back from the original root system.
If your not happy with the growth and plant as the season progresses, fall is always a great time to make some new planting decisions.
Here is a link with more information.
https://www.gardeningknowhow.com/ornamental/trees/sand-cherry/purple-leaf-sandcherry-info.htm