It seems that wood burns best on a bed of ash and only requires air from above (once going) while coal requires an air feed from below to burn well.
Does your ash not build up on the grate after a few nights?
My Clearview stoves are multifuel but after a little while there’s a good 3″ layer of ash to burn on if I don’t riddle it – so the same as a wood-only stove. I just poke a little hole in the ash to allow a bit of air through when I light it.
That said I also have a wood only stove and it looks like your plan should work.