The DB50XG is powerfully loud but your problem sounds more than that - do other games sound OK with this setup? DOOM messes with the mixer to, are the levels OK with that game?

Or do you have a different sound card to try?

Yes, the same problem exists in Doom BUT there is separate volume control for FM and Speech, so I can set music to 40% and digital effects to 100% to make it nearly equivalent.
Privateer respects the settings from SNDINIT.EXE where I also set FM to 40% and digital effects to 100%.
Observation: When I start Privateer, speech and music are set according to settings in SNDINIT.exe. VOLTSR.EXE (Opti's TSR tool for in-game volume control) works in Privateer. If I start Dune2 afterwards, SNDINIT settings are ignored (music very loud, effects silent) and VOLTSR doesn't work (also not in DOOM). If I start Privateer again after Dune2, FM is way louder than during first start. I suppose, Dune2 sets FM to 100%. Normal volume settings (music: 40, effects: 100) have to be restored via SNDINIT.EXE /B after finishing Dune2 to restore correct ratio.

Unfortunately, I don't have other soundcards to test. Only the HOT-235 spare card.

And you're 100% sure you're using the right version of the mixer software? I had a PAS16 acting strangely once because I was using the wrong version, so it might be worth having a hunt around for other versions.

Try these drivers and see if that makes any difference.

They were downloaded from Shuttle's website.

@badmojo, @Joseph_Joestar Thanks for your replies.
These are the drivers that I'm using with my two HOT-235 cards. It seems that they have a problem with sound volume when a wavetable board is attached. I wouldn't say that the card is defective as the problem persists in two machines with two different HOT-235 cards.
I (temporarily) used a dual card setup for testing: The HOT-235 with wavetable board in conjunction with a CT2890 (Soundblaster 16 Vibra with real OPL3 chip) that is connected from line out to HOT-235's line in. This setup works without problems (after I tuned the input/output levels of both cards the right way). But I did not like the fact that I had to initialize/configure two cards at startup and use two different programs.
My new (and hopefully final) setup is an Opti 82C929 based card ("Pro Multimedia" with Multi CD, Wavetable header and OPL clone chip) that does not have the problems (also using the 82C929 drivers from vogons). All problems are gone. Sound volume is the same in all games and FM is not overly loud. Very nice!
In the next few days, I'll get a Shuttle HOT-233 (with real YMF-262!) to put into the second machine, so I can hope the problem is solved then for both machines.

Good to hear! It amazes me how wonky the default levels of some ISA era sound cards are - when you find a card that sounds right without any mixer fiddling it feels like a major win.