My wife plays the pipa, which has lots of awsome frets going all the way down the body, not just the neck, and I say awsome because the ones on the neck are huge chunks of cow horn or obsidian, not just little wires.
Anyway, the low-end instrument I got her to rekindle her interest developed a creep or bend in one end of one fret and it was a little off.
But, she can compensate by pushing to one edge and rolling her finger off the fret and onto the string, essentially holding it some distance from the fret’s position. I suspect you can do the same with a guitar.
Meanwhile, our band features another instrument that has fully movable tips that bridge the strings, and it is re-tuned between numbers. Take a look at the Guzheng! One style of playing reminds me of the steel guitar. That article mentions “Experimental, atonal pieces have been composed since the 1980s” as well.
Update: I happen to have just uploaded a video that shows this feature of the guzheng. The performer explains how the scale used can tell you something about the region of the music, and then retunes the instrument from the pentonic scale to (not stated) on-stage. At the marked position:
Also, note that this instrument facilitates microtone playing by pushing on the string on the other side of the bridge. This does not act as a fret, but adds tension to the string. It’s used commonly for a viberto effect, but she can be seen doing it on a couple notes besides that — presumably to get a sharp or other note that there’s no string for.