Has anyone played with digital delay lines on SKY130? What would a reasonably achievable delay per tap be?

Take a look at the so-called digital PLL in the caravel design (actually a frequency-locked loop). It has a trimmable ring oscillator which, if you unwrap the loop, is in the configuration you describe for a digital delay line.

What's the tap resolution?

My behavioral verilog for the ring oscillator in the caravel repository has these numbers: 23.85ps per trim bit.

~24 ps, OK. Good to know