If you are after accuracy, it's not a bad idea to start thinking like an organization that has a healthy respect for accuracy, like NASA for example.
Or if the objective is to spend lots and lots of time on homebrewing precision positioning gadgets, some casual reading on ASML EUV wafer steppers might be in order.
eBay is literally crawling with inexpensive used encoders with crazy resolutions. This route will save you machine space, time, money, effort, and make your widget better.
Precisely this. If you want to do this for the fun of it, then have at it! If you're having fun while doing it, mission accomplished, that's what hobbies are for. If however your brain is providing you with bullshit rationalizations such as
"I want to create a simple DIY solution anyone can make, using only their local print shop. ^_^", then yeah ... no. If you really believe that, then do the following experiment: go to a DIY astronomy forum and start a poll. Are people interested in making an encoder such as described above. I'm willing to bet the answer
"Not only no, but fuck no!" is going to get the most votes. Why? Not because it's an inherently bad idea. But simply because it's frigging 2019. Why would anyone want to faff about with the local print shoppe for something like this? "Nono, not this usb stick, that usb stick. Nono, not this pdf standard 2.0 sub XYZ/, that pdf standard sub 2.1 QED. If you don't use that version the output of your pdf exporter will not result in the toner placement you intend." <Insert multiple trips to print shoppe here>. Now contrast that with: pointey-clickey-ebay, go about your business until part arrives, integrate part into project. Hell, if you find out later that the encoder you got was not precisely what you needed, there will always be
that other project where you can use it.
So if you need wafer stepper precision,
go aim for it! You won't reach the goal, but your efforts can have a good price/performance ratio. You will learn lots of stuff, and if you post
that as a DIY-howto with parts list, it'll even be relevant in 2020! For anything less, maybe the ebay encoder is a better use of limited time...
Regardless of the encoder... As other posters have already suggested, open loop is probably the way to go. You can characterize the positioning error and compensate for it. The simplest way would be to use a deconvolution filter based on the estimated positioning error. Probably iterative, with a sprinkling of wavelets and l1-minimizers. Or if numberical solutions are too boring, and you simply
have to have something mechanical in the mix, I'd suggest looking into make a rotational flexure, driven by a piezo stack. That can be made pretty damn stiff, and the loads are fairly predictable. At least, I certainly would hope so, if you value your optics.

That flexure would then be placed at the telescope mount, and make minor corrections for any rotation errors caused by the imperfections of the stepper, worm gear, etc. Making such a flexure doesn't have to be super expensive in terms of material. But don't worry! That will be more than compensated for by the time spent in design.
