Got it.

I think you should find a used, entry/mid-range road bike, in the 52 to 56 cm effective seatpost c-t-c range, as big as you can stand over. Preferably with a threadless stem, not too-steep seatpost angle, and sloping top tube. Change stem height/length, add a threadless stem extender, change handlebar type/shape, and adjust saddle position to get your torso to a reasonably comfortable position. Don't spend a ton on it. Don't try to achieve perfect KOPS. Don't expect to do long rides from the start. Don't expect long rides to be entirely ache-free. Wear padded shorts and padded gloves, use padded bar tape.

Then ride, work out, stretch, do yoga, etc to get your fitness up, flexibility up, core strength up, and weight down.

Adjust the bike's position as your own condition changes; for example, even if your lower back flexibility is limited, you can improve your hip flexibility, and gradually lower the bar and move it further from the saddle.

When the time is right, get a real hands-on fitting and buy a different bike or consider having a custom frame made. I wouldn't spend the money on fitting, expensive bike, or custom frame right now, because you are not close to the condition that I presume you intend to achieve.

Also, I wasn't clear on why a recumbent is not an option, but they do solve a lot of fit problems.