I also have switched to the monofilament fly tying thread. I have some 5 mil stuff- two rolls, one black, and one white/translucent. I use it on smaller ships and smaller scale, like 1:700. It looks fantanstic- you can barely see it.
However, that brings up a problem. When I am doing the rigging, I can barely see it- at times it completely disappears, even though I wear 2.25 diopter cheaters when doing rigging. I have found something that helps. I have made to backdrops of foamcore, one white, the other black. I use whichever is the complement to the color thread I am using. When the thread is seen against that backdrop, it is visible. However, when I try to see either thread against the ship- looking downward towards the deck, it disappears if the ship has a medium gray finish! Then rigging gets really hard!
My philosphy has been that oversize rigging is worse looking than undersize, and I always try to err on the side of thinner rigging. But now that I can get stuff that is that thin, I have the dilemma- thread that is too thin to be visible is a real struggle.
In thicker stuff I try to pick color that will reduce contrast, which makes it look thinner (I won't get into the visibility theory on which that statement is based). In thicker threads that give me a choice of color, that is a good way to do it- pick a medium gray or cream or tan color- but that ultra thin stuff does not give you much choice of color.
As a final thought- really good, positionable lighting is really important in rigging small scale models.