My system locale settings (Linux) already have 24h format times.  But the program still displays them with silly AM and PM monikers

Where? The only place I found that shows time is event log but on my system (Linux) it properly shows 24h timestamps.

https://imgbox.com/ttO2AeCU

My event log shows AM/PM too

use https://postimages.org/   for posting image

Nope. No problem there.
Are you in a country that uses AM/PM? Try switcing country in you system setting to one that uses 24h format maybe.