Sheesh — how to find something I'm looking for: write up the question carefully on Stack Exchange, at which point the keywords to search for will be clear in my mind, and I can quickly Google up the answer myself:

It's the Frio Universal Cold Shoe Adapter. It's exactly designed for what I need, and at a little over ten bucks it fits under my price limit, too. So I ordered one; here's the report!

Description

It's a little rectangular piece of relatively tough plastic, with a cold-shoe "pocket" near the front and a flexible clip to hold the flash in place. Underneath, there's a securely-attached metal socket, threaded for a standard 1/4" tripod screw.

Function

It works; my Metz flash snaps easily into place and is held there securely. Until I tighten the wheel on the flash shoe itself, the flash wobbles from side to side a bit, but there's clearly no risk of it going anywhere. Once the wheel is tightened, it's steady.

The clip to release the flash is molded from the same piece of plastic; it flexes down or up to provide the locking. I didn't have any difficulty or frustration working it — in fact, it's easier and faster than the screw mechanism of my existing cold metal shoe. The clip seems secure and it does appear to be high quality plastic, but if you take your flash on and off the clip dozens of times a day, it may wear out.

The other thing worth mentioning is that since the screw doesn't go entirely through the clip, you may want a nut to tighten underneath the clip. It holds well enough without but that would feel even more secure and make it easier to fix the clip so it definitively faces one direction even if bumped.

Version 2

In 2013, the Frio v2 model was released — exact same thing, except it now features a clever dual thread which will work with both the standard 1/4-20 tripod thread and with 3/8-16 as common for lighting equipment, large format photography, and apparently in other European equipment as wel

Value

It's a little pricey for what it is, but that's typical for niche products from little companies. And when compared to the generally high prices for this kind of photo equipment in general, it actually seems within the realm of reason. Given that it seems to do its job so well, I'd say it's worth it for the ease of use and the security for my flash. You can get it with free shipping from Amazon, or get the triple-pack for under $30 including shipping — get one for multiple light stands, or split with a friend.

Conclusion

Yep, this answers my question. I hope this or similar clips become standard, but until then, this'll do.