Medium format door knobs

When I built my Atrium type door, I hit the same problem. I went to the local locksmith and she ordered me a solid brass one out of California with lever handles and a very small footprint. Today with the internet, I could probably avoid the mark-up (that was in the '80s). here is one;

There was a place in NYC in the east 50's called "Just Knobs", and that is all they sold. Even then I didn't find exactly what I wanted for my big wood desk. If they're still around, they might be online.

Most lock manufacturers have adaptor kits for 2 1/4 inch thick doors.

What's a backplate? Is that the metal that goes around the inner door knob? 21 years a locksmith, and I've not heard that term.

sounds like you need an older style door knob/latch assembly with separate knobs, latches, and escutcheons (the part that you are referring to as a "backplate" is actually called an "escutcheon" or "rosette.") My local hardware store actually sells the parts, although you may not find 'em at your local Big Box. I'd stick with a tubular latch as a mortise latch is a lot of work for little payoff unless you are restoring a vintage house and everything has to be period correct.