Tonight I spent a couple hours out in the workshop, and made the halfnut detent arm and spring, and filed grooves on the halfnut rim to accept them. I shaped everything until I liked the feel of the snaps, both engaged and disengaged.
I found I had a little play in the half nut engagement with the leadscrew, yielding backlash, because it wasn't quite thick enough to contact the back of the apron, by .024", measured with a feeler gauge. It was cocking slightly with a change in direction. It is supposed to bear against the apron, so I made up a shim washer that thickness, and then there was no more play at all. The backlash disappeared.
Everything was a little stiff, so I chucked an electric drill onto the tailstock end of the leadscrew and moved the carriage end to end 20 times times to wear the halfnut in a little. Then I checked again the position of the engagement detent to adjust if necessary, but it was fine. The carriage moves smoothly now, the halfnut stays engaged, and clears when disengaged.
I moved the carriage near each end in turn and adjusted the leadscrew bearings up or down to eliminate any bow when engageing the half nut. I haven't drilled for the bearing mounting bolts yet, but they now are both correct in height and clamped, ready for drilling. I might slot them anyway so they can be adjusted up or down if needed.