BTT ^X not working in Chrome Remote Desktop

I have BTT Touch Bar buttons set up for undo/redo/cut/copy/paste, and they work fine in most apps. But sometimes I access a Windows box via Chrome Remote Desktop, and I need (for example) to send ^X instead of command-X for Cut. So I made a new button, just for that app, and configured it to send the ^X shortcut.

But it appears that all the Windows box is seeing is the "x" itself, without Control (i.e. whatever was selected is replaced with an x). Obviously it works fine when I actually press control-X. So whatever BTT is doing to send the keyboard shortcut, Chrome Remote Desktop isn't seeing the modifier key.

Is there any work-around?