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It sounds like what you want is a grayscale mechanical encoder, which you can get from digikey and connect to the digital inputs.
This won't give direction of rotation. But, you can keep track of last iterations value and determine which way you're going.
You just have to make sure that you don't go through more than 1/2 revolution during your cycle. If you are going to go through more than one revolution, you can attach your encoder through a gear.
I don't think there are any infinite turn potentiometers out there. If there are, they probably have infinite resistance too, which would make them incompatible with the RC analog input.
Other legal (last year) ways of measuring continuous shaft rotation include optical sensors, optical encoders, and hall effect sensors. These options are all powered and may require a custom circuit to generate a reading that the RC likes.
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