Turntable equivalent tempo control in Ableton

Hello community,

I was wondering if anyone of you knows of a device or has tried to build anything related, I'm looking for a way to control the bpm in Ableton in a traditional fashion of how turntable is set up as if there would be a engine rotating beneath the clock of Ableton. Basically the device would give the user the ability to move in cents as related to current speed (as the range from most turntable would be -12 cent to + 12 cents, so octaves, but of course in digital domain this could be user-defined quantity).

I know of the nudge function included, I use it often synchronise to analog equipment and it mimics some of the functionality that I'm looking for.
In practical use I want use this to have more organic and non-lineair control of tempo when mixing with warped records. And for me it's also important that is possible to record these tempo changes (as opposed to the "nudge" function). I would hook up the parameter of the cents deviation to a midi-controller or sorts.

Any input is highly appreciated,

All the best,
Robin