My humble opinions

In approximately which year did
: UG switch from the traditional style cases of the 1940s / 50s to
: the case with the Speedmaster-style bezel? [and I do apologize
: for the Speedmaster reference]

I agree that the twisted lug cases are adaptations from the Polerouter line. I have little idea of specific dates, and I think 1960 is correct for their use in chronographs, and mid 1960s is more or less correct for the external bezel models

One convenient thing about UG is that it is possible to date by case number. I have one twisted lug TriCompax without external bezel produced in 1960, and two with externel bezel, both produced in 1966, hence my conclusion above.

Did the transition to the Valjoux
: 72 movement occur at around this same time or did the V72 come
: later?

As I mentioned somewhere above, Zenith bought Martel, the origin of UG's "in-house" chronograph ebauches in 1959-1960, UG having staked its future on its microrotor three hand watches, produced at a brand new state-of-the art facility they had built in Carouge, on the outskirts of Geneva. The UG cal 285 became that Zenith 146, Zenith's workhorse handwound chronograph movement, essentially without modification. I believe that UG effectively lost access to these ebauches thereafter, although they continued to use their existing stockpile of movements until it ran out. The simple chronograph movements were exhausted before the Tri-Compaxes, and UG at some point contracted to used the V72 at that point. Simultaneously, the complicated chronograph line was adapted to a unified look with the Polerouters. Its not a disagreement with Laurent - the UG ebauches could have lasted until the mid-1960s.

When did we first see the true 24-hour indication
: chronographs, the Aero-Compax?

The original Aero-COmpax is not a 24 hour watch, but a 12 hour chronograph with a so-called "memento dial," a fourth dummy dial set by a left hand crown to show a time as a reminder - it was not connected to any actual clockwork. The 24 hour versions are late models, and there are lots of variations, including some from the 1990s I believe. Big mess, as Laurent observes.

An additional note: With all of the focus on the Valjoux pieces, it is worth noting that these model lines antedate these by several decades. The Compax exists since 1936, and the UNi-Compax, Dato-Compax and Medico-Compax soon after. The Aero-Compax appeared around 1941 and the Tri-Compax in 1944. UG was way ahead of the competition in branding and naming model lines. There are literally hundreds of executions of these models, some of them sublimely beautiful although perhaps more traditional looking than the Valjoux powered ones. For a full appreciation of the manufacture, it's important to realize the depth of this history. The ones we've focused on here - certainly appealing - are a last gasp for the glorious company, having completely fallen off the train of chronograph innovations that it once drove. IMO, it only adds to their charm.