Does anybody have a copy of a video converter from the mid to late noughties called MPX Make by any chance?  It was a shareware application which I got bundled on a miniCD with a 1.5" media player from UXcell, though I'm sure it was also available online and bundled with other cheap players.

I could really do with a copy for an artwork I'm making.

You didn't say where you've looked already, but the Internet Archive has two potential sources.

The Software Collection doesn't contain it directly, but if you can identify a magazine cover disc with it, they may have that.

Otherwise, you can do a historical searches - it doesn't seem to do phrases, but it did highlight the now-offline dailymp3.com which is audio-focused but may contain it in its updated software lists, or fiddle with search terms to see if any other relevant sites come up.

The X-Micro Video MP3 user manual says it came with that. The archived X-Micro download page doesn't have a link for the XMP3R, but this dodgy looking foreign driver site has an 11.8MB download that may or not just be drivers/malware.

You could also try getting in contact with random strangers Fernando or BlueSweety3 and see if they have a copy of it

What does it specifically do?
In case there's an alternative that can do similar.

converted videos in since deprecated formats to something still playable now?

If it is that, then I'd hope ffmpeg/avconv or VLC could do the job.

some of the old codecs are copyright-encumbered.

Where there's a will there's a way!

Thanks very much BP! I'll investigate all of those.

Vice versa, Smiffy & Ant: it converts a range of extant formats into MPX, a weird, deprecated proprietary format that will play on the redundant (but rather useful) player. 

What's the player do?

Ah, you're converting to an odd format.

It's a 1.5" player that fits snugly into a cavity in a wood-turning I've made.

Wot's wrong with microsd?

Probably something to do with microsd being a storage medium, not a video player.

In my poking around before, I saw mention that most MPX players also handled ...some other format...

...and in trying to recall what that other format was, I stumbled over this:
https://web.archive.org/web/20100815084506/http://www.kingston.com/support/PORTABLEMEDIAPLAYER/Transcoder.asp

"The PMP Transcoder is the KPEX100 tool that enables you to convert WMV, ASF, MPG, and AVI video files into the supported MPX format."

Had to download via Curl because Chrome sucks, but it did successfully convert an AVI - hopefully MPX is a single format, and doesn't do player-specific codec stuff or whatever...

I need to see a picture of this "player".

Ah. I clicked your link. The *screen* is 1.5". Unfortunately it appears the download link for the converter software doesn't work. Wow, the little fucker even came with *games*.

Cheers for all your chasing, BeeP, I'll give it a go. It's the most promising lead so far. It was definitely a shareware that various firms latched on to.

Particularly shit games, even for the time...

Sorry BP, I'm being thick. I've downloaded & unzipped Curl, but I can't find an executable file.

You don't have the MPX conversion app in a transferable form and size, do you?

https://www.dropbox.com/sh/p9t8qw2wuhb4hyj/AABj9q7HvbkIUCrHvdwyjgsga?dl=0

The setup exe is in the Transcode/English subfolder