How about a half wall, leave it waist high?.. Minding this is not a load barring wall? Correct?....

Other options are to fill the gap with 3/4" ply then run a laminate over the rooms or take all the entire floor up and replace.

Is your floor prefinished? Im assuming so. Todays theres hundreds of different flooring manf. It may be possible to match color or at least get it close. If not theres always the option of of feathering in 2 1/4 wood of the same style the sand and refinish. I guess theres more answers that are needed before a solid answer can be given. But a well trained / experienced floor professional can work wonders. And can make it seemless.

The wall IS load bearing, so there will be 2 columns for support. My main concern was if it was possible to put more wood perpendicular between the two rooms...We have a whole box of the 3" wood,same company, color, etc., because we had our master bedroom done using it last year. That's how we learned the company no longer made the 2-1/4. I just wanted to make sure ANY wood could be laid in the gap, but running perpendicular to both rooms. That way, we wouldn't have to replace any of the existing flooring. Does "feathering" mean weaving more wood in? It's glued down, so can just some of it be pulled up without messing up a huge area?

Yes thats what feathering means. Since its glued its going to be more work but you might find a pro for the right price. Although after reading their quote you may opt for a transition.