Thank you for all the suggestions.
I think a collet stop may be the first thing to try although these are 3C collets in a 9C lathe.
My 3/32 collet had a stop when I got it, but I have never paid much attention to it. The stop is a plug with an external fast spiral and was apparently driven into the back end of the collet, and has a hole about 1/4 - 20 for a stop screw.
My preference, since 3 C collets have no internal threads, is to make a plug with a threaded hole and set it with removable Loc-Tite. Even that might be more than I need to temporarily hold a stop in place.