DIY linear servo mechanism?
The rotary encoders for linear gantries will ruin your 20 microns (You possibly are mistaking the stepping resolution to absolute positional accuracy). Rotary encoders can only be used for velocity feedback loop. Positional reading should always use tape.

For 0.1..1.0 microns reading use those expensive invar tapes with envelopes, glue, reader heads and homing markers. Do not use limit switches as homing reference.

Well, the cost of good 1 micron tape based setup for linear motion can cost $1K.
I do not defend the greed of monopolists in motion industry, but what you can possibly do ? If you can build your own lab with tapes, rubies, optometry, granite tables etc, then you may reach the cost of below $1K per gantry after few years of trying. But who wants to try it ? There is no shortcuts, unless you can live with very very slow motion.

For very very slow motion you can invent tons of solutions with capacitive readers like on calipers, induction readers like in scales, even some cheap laser interferometer etc. But this is every time a self serving science, which is impossible to reuse.

One thought about cheap tape is using cheap microscope camera reading a unique pattern on long tape with search algorythm based on calibration against reference tape. But this will require massively fast CPU and gigabytes of memory. Which means slow, again. Every normal motion needs a response in microsecond or less.