You really should find a focuser with threads if you are going to all the trouble and expense.
What size imaging sensor? It needs to be small to do this.
You need to change backplate if you are going to go with APS-C or Nikon DX size. That's not what I mean by small. APS-C and DX are LARGE.
The Biggest focal reducers offered by Celestron do not support above APS-C without vignetting..
Yes, you can read the specs on the big $850 FR and the big ones do have 60mm aperture, but they only support a 42mm interface and at 146.5 mm backfocus don't expect miracles. Remember that the reducer concentrates the photons into a smaller area so the 0.7x reducer takes an images circle that starts at 42mm and it ends up as 29.4mm. That's just enough to cover the DX diagonal of 28.8mm. and you must consider about a 50% energy drop-off as the higher ncident angle light gets cut off. So for Focal Reducers other methods are needed.
But the OP didn't say there was a FR involved.
But Edge HD isn't a simple SCT. It's more like Petzval refractor. An additional set of optics sits inside the baffle and does 0.x flattening.
That's why the backfocus is so restricted and really must stay at 146mm +/- 0.5mm from the rear of the scope for AP. It doesn't matter where the external focuser sits. The OP has it correct. It can only be used for microfocusing. That's in the +/- 0.5 mm realm. It might add some flexibility too in avoiding the issues encountered with small 1mm or 0.2 mm shims.
So without a FR what matters is clear internal aperture and the ability to identify and repeat a midpoint location on the external focuser as a zero point. That means electronic focusing.
Why? Because A) you need to focus both directions B) The zero point is your 146mm point and you need to be able to calibrate and repeatedly find this position on the focuser.
Check 1st the actual clear aperture at the back of the scope. You may find surprising field stops where you least expect them. The SCT threaded interface on the back of the telescope is about a 39 mm clear aperture.
The conventional FR that threads on is 38mm.
The 2" visual back is 50.8mm whatever you connect to it will at best have 48mm clear (for a M48 filter thread and the thread stop brings you down to 47mm maximum. Many adapters are much less as 47 mm clear on a 50.8 mm interface is a very very thin wall of 1.9mm
Most will be closer to 44mm which is all you expect out of a M48 " 2 inch" filter.
You can see why you need to measure. What's the point of an oversized OAG if through the focuser you're down to 44 mm?
So you can start with sensor size or start with the scope and figure out what you end up with at the other end. Do it on paper 1st if you can but you need clear aperture info which takes some digging. Since you have the back of the scope and changing things gets expensive, I would normally suggest you start there and keep everything threaded. If you end up with too small a sensor for your purpose or have a specific camera in mind to stsrt then you need to start at the imager and work the other way. Trust me, you'll find if you have a taste for the new large sensor cameras they cost a lot more to implement than you might think.
If you want to go full frame, IMO the best option is the Astro-Physics 2.7" system. That will leave you at 48mm to the camera if you're careful to avoid the T interface defaults. But 1st check the scope baffle or in the case of the EdgeHD the rear optical path for clear aperture to be sure it will support the final image circle. Don't be surprised if it's not supported. The SCT designs are all based on M42 which is NOT full frame.
Revisit the focuser choice after you know what clear aperture you need. You will need electronic focusing and threaded interfaces throughout.