No Jeff, that's nonsense. Copper tape or aluminum foil tape will not hold up to the pogo pins rubbing on them. It'll last a few rotations before it wears thru, or folds up the tape, or pushes it off the substrate, likely creating another short.

I do like the slip ring idea if there is room and a way to secure it.

Otherwise, get the original gerbers, or recreate the gerbers in a PCB cad program, Eagle would do this easily. Then consult with a domestic PCB house on how to specify the copper thickness and hard gold plating. Doing it by design rather than some photocopy process would insure correct alignment with the pogo pins.

A "dry" connection does not imply no DC, by the way, it implies very low current.