Thanks to @DanielPiker’s “dirty double data dam trick” (“naughty loop” in red group), this is weird but seems to work! Though it is cumbersome…
INSTRUCTIONS:
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Set Value List (blue group) to “Choose” and use the ‘Choose’ slider to select one point.
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Set Value List (blue group) to “Move” and use the MD Slider to move the selected point.
move_save_points_2023Jun21b.gh (25.4 KB)
The reason for the Value List switch is to suspend metahopper from resetting the MD Slider so it can be moved.
As I recall, the similar idea I had years ago (on the old grasshopper3d.com forum) was a way to index saved states of a cluster. It could have any number of inputs (like sliders, rotate angles, value lists, etc.) and when the index value is changed, the control inputs would be reset to the saved state values. 
UPDATE: Two minor cosmetic additions:
- Added “MODE” label to Value List (blue group)
- Added Point List to number the points.
In the process, I noticed that points 0 and 8 are duplicates.
move_save_points_2023Jun21c.gh (23.5 KB)