According to your picture (outside industrial usage), I'd definitely avoid usage of a measuring method based on mechanical contact or optical principles.
The first issues I see in the overall story is the requirement not to use RF communication... Hopefully (for you), this one can be changed.
Hall effect sensor could be a solution, but due to a metal construction, it might take some trial & error attempts to find a location for a magnet (or a durable spacing material between the magnet and the metal rotor) and the sensor.
Since the connection wires on such machines are always weak link of the overall product, what I'm thinking about is an option to create an autonomous sensor (one molded mini brick) containing sensor element, tiny microcontroller, a rechargeable battery and just two charging contacts exposed to the outside world. The sensor would measure gravity vector (by rotating it around horizontal axis, the gravity change represents its current angle / you can count rotations). This measuring box would burn very small amount of energy, so charging it once per month or so can easily be achieved using a small battery pack...
To decrease overall costs, the reading/display unit could be a mobile phone running a simple app, for example...
There are quite some options how to solve this challenge... however, try to avoid wires and mechanical moving components.
Best wishes, Ivan Zilic.