I'm not sure if this is what you're looking for, but this is how I would implement a universal tab notation for string instruments (including fretless ones):
The note or interval for each string is specified, and instead of fret positions, an interval notation that is as universal as you want it to be is used.
For example, one could specify a guitar string tuning as E A
B E, and write 1/1 21/16 7/4 35/16 3/1 4/1 in front of the respective strings in the tab.
Instead of fret positions, one could either use frequency ratios, or degrees of a predefined scale that can be modified with accidentals.
For example, one could define that 1 2 3 4 5 6 7 8 refers to the pythagorean diatonic scale mode LLsLLLs, expressed as ratios: 1/1 9/8 81/64 4/3 3/2 27/16 243/128 2/1. The 5-limit major scale 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 could be denoted as 1 2
3 4 5
7 8 on a single string.
(I personally prefer interval notations where 1/1 corresponds to 0, though)
Another option for an interval notation would be to use degrees of some kind of "chromatic scale" that is large enough that no accidentals are required. For example, one could identify each scale step in 53-EDO with a specific just ratio (or a tempered interval, if a specific temperament is used), and simply use those numbers instead of fret positions.