Welp, I have come up with a solution that seems to be working pretty well *AND* does not need 3rd party software.
It is extremely complicated to set up for what it's doing. But basically:
I made an apple script for each function of the keyboard I wanted to use, which for me is just the three iTunes buttons plus the three volume buttons. I'm on a Mac mini so I don't need brightness buttons, and I use hot corners for Mission Control so I don't use those buttons either. Which is good because now I can add more things to those buttons if I need to down the road.
In System Prefs > Keyboard > Keyboard, I checked the box to use FKeys instead of special printed functions.
This is where it gets complicated, and you will need extra instructions. I used this link but another one might work better:
https://apple.stackexchange.com/questions/175215/how-do-i-assign-a-keyboard-shor tcut-to-an-applescript-i-wrote
You have to use Automator to turn those applescripts into custom "services"
Once you do that, you can go back to Keyboard System Prefs and set up shortcuts for each new service you created. The special keys are now regular fkeys so you can link em up and you're good to go.
Well maybe. When I first did this, it didn't work. I rebooted, the fkeys still didn't work. Then I seeked out my services in the actual "services" menu under the Application menu. They worked. Then they started working through the keyboard. Weird!
But now everything is working quite well. The only two quirks are no onscreen feedback for adjusting the volume controls, and I made it so up/down increases the volume by 5% instead of 6.25%, which is the 16 sound levels the default volume controls give you. Hopefully it works and keeps working. If so, it will be good enough for me.
Also since applescripting is the least-intuitive programming language ever (which is ironic since it specifically tries to be the most intuitive), here are the six applescripts I used:
Play/Pause iTunes
tell application "iTunes" to playpause
Next Track iTunes
tell application "iTunes" to next track
Previous Track iTunes
tell application "iTunes" to previous track
Increase System Volume
set currentvolume to output volume of (get volume settings)
set currentvolume to currentvolume + 5
if currentvolume > 100 then set currentvolume to 100
set volumeoutput volumecurrentvolume
Decrease System Volume
set currentvolume to output volume of (get volume settings)
set currentvolume to currentvolume - 5
if currentvolume < 0 then set currentvolume to 0
set volumeoutput volumecurrentvolume
Mute System Volume
set arewemuted to output muted of (get volume settings)
set volumeoutput muted (not arewemuted)
