It is kinda possible to get keyboard events go into the Redux window with Reaper:
Does the ‘technique/workflow’ suck? Yep, but I didn’t write any of this.
In this example I’ve used a virtual keyboard (no, not the virtual keyboard in Reaper) called ‘xvkbd’ to inject the keyboard events. Video above shows that it can be done.
I forgot to mention: A similar technique should work/can be made to work in Linux Ardour as well.