When you install the drivers, are you installing the DOS drivers, or Windows 3.1 drivers?

If you need 3.1 drivers, go here http://support.creative.com/Downloads/welcome.aspx and download one of the 3.1 driver packages.

Both the DOS and 3.1 drivers are installed, it seems, as the SB16 drivers show up in Control Panel. I also have the SB16 programs in a group in Program Manager.

I'll attempt to uninstall the Avance drivers (all of them) and see if that does anything

Okay. One you do that, I recommend that you uninstall the sound blaster drivers as well, and then reinstall them. Good luck!

Sounds like an IRQ or DMA conflict to me.

I have no idea how IRQ and DMA work, but when I open Audio Card Configuration in 3.1, it tells me the IRQ is 5, low DMA 1 high DMA 5.
I have a SIIG parallel and serial ISA card installed. That could possibly be causing this, but I like it in there, so can I set the IRQ/DMA to something else?

I removed the other Avance driver, the Avance OPL3 FM Synthesis driver. There is another one, Avance MPU-401, but it tells me it's a driver required by the system - so I might not mess with that 🤣.

You'll need to do a bit of reading on IRQs and DMAs then, because it is absolutely critical when working with these old systems.

Effectively, each device needs its own IRQ (Interrupt ReQuest) and DMA (Direct Memory Access) Channel. (there are exceptions where sharing IRQs is permissible, but generally you should avoid it.

Different devices will use different IRQs. Each Parallel port, COM port, and Sound Device will require one. The Avance MPU-401 may be causing that MIDI error you're seeing because MPU-401 is the interface used with MIDI devices. Have a look in the BIOS to see if there are assigned IRQs there. Keep track of all of them, so you get an idea of which device is using which IRQ. Sound Blasters should be on 5 normally, and the MPU-401 should be on 2. You'll likely have a COM (Serial) port on 3 & 4, but you may not need those.