You can do this best in Karabiner.
There are so many similar example modifications for this scenario.
From windows to mac to virtual machines and back.
On this leven in the system Karabiner is your friend. And it will never be in the way with KM and viceversa in my experience.
You could connect a 2nd keyboard to your computer.
Map every letter on that keyboard to Mouse buttons 3 to 28. Then Keyboard maestro will see these commands as mouse buttons. You can use any modifier key as always while adding a F10 or F11 to a single press. Keyboard Maestro will register this as F10/F11 presses. The combo works perfect as they are on different levels in the system.