The various scripty fonts for sports uniforms would seem to satisfy your criteria, but I don't think that's really what you're looking for. They're all mean to be embroidered and read at a distance, and are very klutzy. Because of their broad strokes and large counters, they reduce very well. See such as Nick Curtis' TeamSpirit, Letterhead's Pilsner, Jawfonts' Fenway Park, etc.

A good suggestion, HVB, and "legible from a distance" is a key requirement, but you're right, I'm looking for something less casual and more elegant.

Donald Young's "Young Gallant" would be a good candidate if the strokes had less contrast between thick and thin:

And Jess Latham's "Fancier Script" is pretty close, but I think I'd prefer something just a touch less casual and more elegant:

A good place to visually scan lots of script fonts is Mike Yanega's Bowfint Printworks Script ID guide, at:

http://bowfinprintworks.com/ScriptIDGuide.html

http://www.myfonts.com/fonts/marksimonson/lakeside/

Check out the products of Sudtipos:
http://sudtipos.com/home

What you are looking for will be there.

That’s Doyald Young, not Donald. Easy to miss.

Wow, thanks for opening my eyes to the full work of Sudtipos and Alejandro Paul. And thanks for the correction on Doyald Young. But the closest I found to what I want is Altast Greeting, which was in the Bowfin Printworks index HVB linked to:

There are issues with it: It's a free TTF and not all the connectors connect properly, but it has basic, classic shapes, a high x-height and wide counters. I had to add some weight to it so the connectors weren't too thin, but that's easy to do. It's not entirely timeless, in that you can tell it comes from a previous era, but it doesn't feel terribly out-of-place today. It could use a little work.

Still, I'm surprised I can't find something like this from a major typographer. Someone could create sort of the Gotham of scripts in that it's so basic, unadorned, classic, timeless, versatile and well-crafted that it's just the standard script that everyone should have a copy of.

Something like the Shelley scripts, then?

Well, Shelley is centuries old, and you can tell. Altast Greeting also looks a bit dated, but at least it looks like it could theoretically be the work of someone who is still alive today. Ideally, I would want something that looks both current and classic at the same time.

Using that Cadillac lettering as a starting point you will end up with a font that is too regular, which implies a lack of legibility — a logo is something very different than a bit of text.

When you say "regular," what do you mean? And how does this regularity imply illegibility?

Regular in the sense of similar and repetitive forms. One needs some differentiation between glyphs to recognize them — hopefully instantly. Example: two lowercase u’s could be mistaken for a w and a dotless i, etcetera.

A logo breeds familiarity due to repetition (advertising, fleetmarking) and gets its own persona in time. You may have seen experiments where certain words or texts were rendered in the style of famous wordmarks, where recognition trumps legibility, eg:

Oh, yeah, the "uvw" is confusing and could use some work, but those letters don't normally go together. Otherwise, I thought the font was quite clear, especially for a script. Still, I'm not saying this is my ideal font, but it's close.