I tried Courier Chess with Fairy-Max, and I was a bit disappointed in it for the reasons you mention. It is a lot better than Shartanj (which is absolutely awful), but it is still a pretty slow game. I was playing with the rule that Pawns promote to the worthless 'Ferz' Queen always, (the actual promotion rules seem to be unknown), and that doesn't really help to decide the game.
If you like historic Chess, I can recommend Grande Acedrex, described in the Alfonso codex published 1283 AD. It predates Courier Chess by nearly 300 years, but it was far ahead of its time. It also has Bishops (called Crocodiles there) and Rooks, and did away with the Ferz Queen and the worthless Elephants. Although it did not have the modern Queen, it has a piece nearly as strong, the Griffon, (basically a double-barrel Rook), and another piece stronger than Rook, the Rhino/Unicorn (a double-barrel Bishop), and a piece nearly as strong as Rook, the Lion. The weakest piece (a (3,2) leaper called Giraffe) is only slightly weaker than a Knight on the large (12x12) board. Promotion is to the piece that started on the promotion square, so there are plenty of decisive promotions.
I have configured Fairy-Max to play Grande Acedrex now, and it does seem a quite exciting game.
Courier Chess was an evolution of shatranj that was co existent with modern chess around about the 1450 to 1550 time period, but gradually was eclipsed in favour of modern chess.These days it's mostly known through a painting by a Renniasance master
Professionally made sets are very rare and extremely expensive so I decided to make myself a smaller scale version using modelling clay! It's a bit rough looking but I think it captures the look to some degree
I use the Zillions Of Games program to play it as well as other chess variants. Overall I think it's an improvement on shatranj as the couriers (whcih move like modern bishops ironically) make it more dynamic, and there are a few more pieces and a larger board. However I still don't think it has the same depth as modern chess. The Queen is very weak compared to todays gaem and there is little incentive to promote a pawn. Still a lot of fun though IMO! Games can last a long time and have an epic struggle feel to them.