My J/P combo only has 12" capacity so I'll be gluing up multiple boards to achieve the dimension I need.
This would make me lean strongly into veneering as an option.
My reasoning for that is : when those panels get glued up, the odds of a perfectly flat and even thickness panel aren't going to be great. So you probably need to think about gluing up a little oversize and bringing it down to the final thickness. Progressively will likely mean greater stability.
If you had 15" planer and a 12" jointer, you could work around that with a piece of MDF and removing the guard on your jointer.
Alternatively, you can use a plane to bring everything square, flat, and out of twist, but that's a fair amount of technique. If you're comfortable with handplanes, you can likely get very close to flat and within a couple thou consistency of each panel. It will probably move more than that, and w/ a few mm reveal between the door and frame that's not going to bug you too much.
With veneers, you would have a different challenge in learning to joint + seam the veneers, planning your layout, and getting a feel for the lamination process. Edge banding wouldn't be a big leap in terms of what you clearly can already do very well.
For a door this size, I don't think glue is going to be a big deal. You could use a PVA veneer glue, epoxy, PU, or UF and they should all be fine for your purposes.
The hardest part if you don't have a pump is the actual pressing.. you need a lot of clamps and a lot of cauls to get pressure everywhere, and that can be a logistical challenge if you don't have a willing helper. But even that is solvable with some fixturing to hold things in place.
Also, the horizontal lines of the room would be complemented with a horizontal grain on a horizontal object.