Thinking to simply things, I uninstalled Karabiner Elements and set up the BTT Hyperkey, following the instructions at Defining a Hyper Key · GitBook as best I could. However, several Keyboard Maestro macros that were triggered by Hyperkey combinations have stopped working properly.
For example, while my Caps-Lock-H still works (pulling up my OmniOutliner help sheet via a "Display Text in Window" action), the Caps-Lock- ←→ ↑ ↓ triggers that call "Select Menu Item" actions to move rows left/right/up/down have stopped working. The highlight just moves around, while the rows stay in the same place.
In OmniFocus, a Keyboard Maestro macro has toggled a star icon at the end of a project's name with Karabiner, but with BTT it starts a sequence to quick to follow that ends up with OmniFocus in a Find screen and an empty Alfred snippet window on top of it. A little frightening, since I don't know what's happened with my OmniFocus data.
BTT 5.553. Running Catalina.
I've attached my setup screens, in case I did something wrong there. Thanks!