In theory, theory and practice are the same. In practice, they aren’t.
I’d experiment and go with what sounds best.
You’ve got ’amp’le power (pun intended), so I wouldn’t worry about any claimed strain on the amps, or your speakers.
I’ve heard many systems that use a sub with full range speakers being given full range signals and they have sounded just right.
All this hand wringing over poor little speakers and amp strain is over blown.
Deal with the room, get your speakers and sub placed as best you can, spend the time to adjust the sub's phase and xover - then just enjoy the music and quit stressing.
imho, of course.