Well not sure it counts as it was neither a rival nor did it actually go into production (only around 15 produced), but the RR Eagle 22 was designed for use with contra-props. Only ever fitted to the Wyvern TF-1 which first flew in 1946, it was a 24 cylinder H block monster rated at around 3200 hp.. but was sadly overtaken by the then new breed of turbo-prop powerplants.

Does make me wonder though that if one of these Reno racing teams unearthed an example that could be made to run, would they have the balls and money to fit it to an airframe.? Wishful thinking i guess..

Pictured is an impressive working model of an Eagle.