You could try this mechanism (please pardon the mspaint drawing):
Notice how the inner shaft has to rotate more than 360 degrees to hit both limit switches. You can use multiple stages to get more rotations.
There are many options:
convert rotational to linear motion through a screw
digital encoders (absolute or incremental)
If you need less that 5 or 6 turns you can use a gear box with a single turn stop. The gear box will reduce 5 turns to 1.
Regarding the use of multiturn potensiometer, IMHO is a viable option. The added ...