Borrow a (or even buy a cheapie) sit-up-and-beg, upright style bike to try.... if you really think that's the solution (to an old back). I'll bet you won't find relief.

Being an old man with a bad back myself.... Just mowing my grass on my riding mower can make my back hurt. Because my spine is forced to absorb every little jolt or shock as I ride around sitting upright. Those little pads between the bones just don't have the pillowy cush they once had.

However.... I have found that a properly set-up and fitted road bike doesn't transfer shock or stress to my back. I do like the brake hoods nearly level with the saddle. And I try not to let myself be too stretched-out ether. But otherwise my set-ups (I have more than one road bike) are basic normal standard road bike cycling fair. My bikes look normal with no special alterations.

I do, do a few core exercises (likely some of the same ones the therapist tried to get me to do) in the off season. A stronger core... makes almost everything better/easier. But the slight soreness I experienced at first while cycling was more than worth the benefits I've since enjoyed.

When done correctly.... your weight and all the jolts and road shock... will be more or less equality transferred to "the three contact points". Those points being your feet, hands, and butt (or handlebar, pedals, and saddle). Notice... none of the points are your back. When in a sit-up position... I can assure you your back will be where you'll feel any pothole or obstruction.

Be sure to "perch" yourself on the bike... properly distributing the weight. Do stand up and pedal every few minutes. bend your arms at the elbows. Try to stay loose and limber.