Inverted Trackpad resets

I've been using BTT primarily to invert my trackpad for a couple of years now.

It's great, I just have one problem with it: When any other app records or shares the screen the trackpad "flips" back to normal orientation. I then have (using an inverted trackpad) navigate to BTT and the trackpad settings, un-check the "Invert..." box and re-check it to get it back to normal.

This can be a little embarrassing on conference calls where I need to share my screen and the first thing I have to do after they can see the screen is to go through this process.

I assume that this is probably a technical limitation of the way it's being implemented and can't be "fixed" so I wondered if there is a way to create a shortcut to toggle the option instead, so I can trigger it without having to navigate around my 27" monitor with a trackpad that is upside down?