Congratulations greenglass! It's not the easiest test to master.
I made this water thickness tester for testing water thickness (only 10 minutes work). I bored a 1/2 inch hole in a block of maple, nailed in 3 aluminum nails, cut off the heads and filed them smooth. I can zero it out on a flat glass. The micrometer barrel has a ball tip so I back it out, set it on the glass under water and slowly screw it in. When it touches the water it is easy to see repeatable to a few thousandths. I set up an 8 inch flat and measured water thicknesses to see which was best. Here are the results in inches:
.110 fringes too wigly and not much dampening
.052 better dampening but still a bit wigly, useable
.035 best overall, good dampening took about 15 seconds
.020 not useable, leveling took way too long
Looks like around a millimeter was the best, this may vary with size though. This flat was pretty good except for a rolled edge and I counted about 8 rings without the collimator lens so I think it might be possible to work up a method without the lens.