After a close study of the rule, and particularly the sample illustrations on page 79 (I think) of the handbook, I believe there is a solution.
There is nothing in the rule that says you must be standing up straight, with both feet on the ground when dropping. The illustration shows the drop with one knee on the ground as acceptable. Therefore, I cannot see why you cannot sit in your cart with one leg on the ground, and drop the ball from that posture. My assumption is that almost everyone with back problems will use a cart anyway.
One of my playing partners was a guy in his 80's who had big problems dropping from knee height. We concluded that he could use his cart as support in order to comply with the rule.
My first game under the new rules. I forgot my stopwatch, to check the 3 minute search rule and the 40 second per shot rule. I reckon the group in front broke both time barriers multiple times.
Everybody, in any group I could see, was struggling with the knee high drop rule. Assessing knee height seems to be harder than it sounds. 3puttpete would have been proud of me for making my other playing partner redrop because he committed the heinous sin of dropping from about mid-thigh height.
Generally speaking we left the flag in until we were within 10 feet or so. A few times I gave up and left it in for my tap-ins.
My club is not playing the local rule for out of bounds. So there could be a few walks of shame still taking place.