The 29 body with the concave rear window roof on the 1969 to 1971 was basically the roof sheetmetal of the four-door hardtop mounted on top of a two-door body. Not sure, but I would say it outnumbered the sportier-looking 23 hardtop in sales. Perhaps this is due to the Fury being in competition with full-size Chevrolet models. The Chevrolet Caprice two-door had been around for some years marketed as something along the lines of a personal luxury coupe (rather than a sporty two-door as was offered in the Impala line) and it, too, had a more formal-looking roof line.
So I guess the 29 body/roof on the Fury two-door was generally perceived as being more prestigious than the 23 body/roof (not to mention that the 29-bodied Fury III cost $20 more according to the price list) at that time. It offering more rear-seat headroom might also have been a point in selling the 29 models.
Now to Analog Kid's question concerning the 1972 Furys:
Plymouth continued to offer two two-door hardtops for 1972. One was the regular two-door hardtop which was all restyled. Although referred to as "regular" it was the one style that was even more formal looking (at least to me): The leading edge of the C-pillar was almost vertical, the C-pillar pretty wide and the rear window size was unique compared to other body styles (a few inches larger than on the other hardtops). Since this styling required a quarter panel all of its own anyway it received "dual sculptured lines" in the front and rear of the rear wheel opening (love them or hate them).
The other body style did, again, use the roof sheetmetal of the four-door hardtop mounted on a two-door body. Consequently, it was again called the Formal roof, despite not looking that formal. The C-pillar was not as wide and raked more forward, plus the rear window was a few inches smaller. It used the overall design of the quarter panel of the four-door hardtop and that only had one sculptured line ahead of the rear wheel opening.
This image in the data book shows the differences and similarities pretty good:
17,545 of the 1972 Furys of the 29 variant were built versus 37,044 of the regular 23 body style two-door hardtops.
Note that from 1969 until 1972 the same system was kept: 23 bodies had their own roofline and were just referred to as hardtops while 29 bodies used the four-door hardtop roofline and were called formal hardtops. In 1973 there was no 29 body style anymore. The term "sports hardtop" was not used during that era.