How about forward gears? When you shift from N to D, does it catch immediately and start moving the car, no hesitation? When it upshifts from 1 -2-3-4 as you accelerate, does it do that smoothly, no hesitation, and no engine racing in between gears? If the forward gears are working ok, maybe it is just a problem with the reverse. that could be just a solenoid or something much less expensive to fix than a transmission rebuild.
One more piece of data: I have a 70’s Ford truck w/C4, one day at about the 120 K mile mark it started to act like yours is doing, but when shifting from N to D. I could get it to engage by waiting, trying again, etc. But over the course of a couple weeks it was getting noticeably worse. A transmission rebuild is what it took to fix it. It’s been fine since, 30 years later.