OK lets try and solve it the other way round.
Modify Omnifocus preferences for the short cut that brings up this window instead of using F19, say CMD+OPT+O. Then use Keyboard Maestro to map your prefered hotkey combo e.g. CMD+Q to type that keyboard combo CMD+OPT+O for you.
I am sure my colleagues will come up with a better solution though.
The omnifocus manual at https://support.omnigroup.com/documentation/omnifocus/mac/3.4.5/en/capture-methods/#quick-entry
says
## Quick Entry
With an easily configurable keyboard shortcut, you can use Quick Entry from anywhere on your Mac to add items to your database as long as OmniFocus is running. Make sure the shortcut in OmniFocus General preferences is what you want, and it’ll open the Quick Entry window no matter which app you’re viewing in the foreground.
You may also like to look at (if you have not already done so)