The point is: Apple does not distinguish between left and right modifiers. Keyboard Maestro, which you also use, does not either.
Only BTT does. It only works if the shortcuts are set up with BTT. That's the downside, if you want to look at it that way.
But then surely more reliable, because no complex mixture of modifiers has to be kept down, but a "real" modifier is used.
I just realized I’d still need BTT. BTW, I set up a fresh "test" account, set up the BTT caps lock hyperkey, and tried it with F9. Just like my main account, it worked when I held down Ctrl Sh Opt Cmd F9, but not with the caps lock. I'll see how Frank1's idea works for me.
I'm trying you idea, but when I record a shortcut in BTT, it displays ^F9 whether I'm holding the left or right ctrl key when I hit the F9 key. Is there somewhere in BTT I need to activate separate control keys?
No, not necessarily. Just trigger your KM macros with a right control shortcut in BTT.
I just saw the checkbox to differentiate L and R mod keys, and now I've got it where on my big keyboard R ctrl plays/pauses the music and L ctrl just gives a system beep.
But it doesn't work when I hold the caps lock, even though I set it to be Ctrl as your screenshot showed. But if the keyboard modifier settings are sending "^ Control" with both the caps lock and the control key, how does BTT know the difference? Or does the Mac send separate code depending on L or R, even though the keyboard settings don't appear to differentiate?
That's for Andreas to answer 
I'm not sure I understand the rest. If you want to perform different actions with left and right control, you have to set up both shortcuts separately.
I guess it doesn't matter how BTT can tell the difference. But I'm at a spot where R ctrl F9 plays/pauses, but Caps Lock F9 does nothing, even though I've set it to perform Ctrl as your screenshot demonstrated.
It seems the Mac gods are stopping me at every turn. 
Did you disabled the hyperkey actions in BTT?
Tried it with the Caps Lock Act as hyperkey disabled and enabled. Didn't work either way.
I have to leave now, but I'll continue later. Thanks for all your kind help!
I think your problem might be, that play pause doesn't like to be combined with some modifier keys.
You can try this:
That fixed it. Do you know of any other BTT actions that don't well with certain modifier keys, or is play/pause an unusual case?
Thanks,
Russell
Got it working with the solution Andreas sent. Seems the play/pause action is unusual.
it’s only some special keys like play/pause. For standard shortcuts BTT handles this automatically
@Andreas_Hegenberg My shortcuts with the distinction between left and right modifiers still work very well, as they always did. An error message sometimes occurs when setting up these shortcuts, if short/long press is added. But if I just continue, the shortcuts work as expected. So no problem at all, just to let you know
Adding a late note here: I had gone away from BTT when I got a laptop without a touch bar, but came back when I heard that it had Hyperkey built in. I came to the forums looking for the solution and then found it through some more exploration.
Instead of mapping the named action to the Caps Lock key, I just had it call the Toggle Caps Lock On/Off action. It works perfectly now!
