I think this magnet pattern works. This is a single species of block that can be flipped around to mate with itself with the proper stagger, and can be shifted left and right by two turns. This is a top view, showing the pattern:
The actual magnets should probably be placed on the side along the second helix from the bottom, so blocks of any height will snap together. This is 12 magnets for a 6-turn block (one magnet per turn per side) which is a lot, but I think that's the minimum to get the snaps that we want.
I think this works??