Strange, we've only ever had it happen on Retina/4K/5K etc. It currently affects my M1 Macbook so it's not a non M1 thing.
Try this - disconnect the 4k screen, then go to your user Library/Preferences folder and delete the com.pgmusic.Band-in-a-Box.plist file from there. Then go to your Band-in-a-Box folder and rename the Preferences folder to something else (for backup), then run BIAB. It should act like it's on a new computer - see if the save/open dialogs are huge again.
After trying this, you can delete the new Preferences folder and rename the old one back. The deleted plist file doesn't need to be restored.
Thanks Simon, I'll try that. It'll take some time because I have to find a monitor around here that has the right video port(s).
I also have a MacBook Pro that's not exhibiting this problem - heck, for grins I might just pull the preferences folder from that one and put it on my Mac mini. What's the worst that could happen?

Don't know if this helps you, but I also don't use a 4K monitor. I don't THINK it is, anyway. It's an ultra wide (LG 34UC88), so it's still high enough resolution that it might still reinforce your theory.
Thanks for your responses!
- Fred