A one evening turntable bash

[Sumpter250]

Might I suggest a solution that mimics the old, tried and true "knife switch." Such a solution could be developed to both convey power to the rails as well as align the rails properly for entry onto and exiting off of the turntable. Polarity could be handled by a toggle switch between the power source and the "knife switch."
It's not elegant ... but it should solve the problem simply and inexpensively, as well as provide a positive method of aligning the turntable tracks at the same time.

Elegant......yeah, not.
Sliding rail joiners, could actually be considered "elegant", "simpler", and decidedly less expensive......and....infinitely renewable, and providing both electrical contact, positive track alignment, and polarity controlled by the table approach track. Most importantly: Sliding rail joiners, strictly adhere to the K.I.S.S. principle.