Instead of a limit switch a hall effect sensor with a moving magnet is an optimal soltuntion since it is contact less there will be no frictional side effects on your application.
But there is one more better way to it, try to use an rotary encoder, something like a 400/600 ppr should also be fine for this, doing this way you have more positional data of the turntable,
You can calculate no of turn, arcs etc.
- A 400ppr would give you a resolution of 0.9 degree per pulse, and
- 600ppr would give you 0.6degree per pulse of accuracy.
Although you can go for even higher ppr encoders but you can get these at very low cost.
Pic from: https://m.ebay.co.uk/itm/400BM-Rotary-Encoder-Module-LPD3806-360-6mm-Shaft-Arduino-Pi-Flux-Workshop-/112607725039?_mwBanner=1
Note: Just an example, price may be different at other webites, haven't checked the price while writing this solution.