Shortround6
Major General
No need for miracles
The XF4U flew for the 1st time on 29th May 1940 - maybe Army just then became aware that (X)R-2800 really deserves attention? Navy was sure about the R-2800 already in June 1938, when they signed a contract covering the future F4U. Even in case the Army decides in mid 1939 to give a try with a fighter based around the R-2800, that gives an extra year. The Army have had enough 'faith' to order the R-2800-powered bomber, from the drawing board, in Sept/Oct 1939 (quote from Joe Baugher's site):
Except that the F4U was extensively redesigned from XF4U to the F4U-1 and such was the 'pace' that both Goodyear and Brewster were brought into the production program over 6 months before the first production F4U-1 flew and mock-ups of the night fighter F4U-2 were being inspected 6 months before the F4U-1 flew. 2nd production F4U-1 was accepted by the Navy by July 31 1942. At that time 81 P-47s had been built. People now want to divert Chance Vaughts engineering efforts from getting the F4U into production and service with the Navy and have them design alternative wings if not fuselage for an "Army" version. Just leaving the hook and catapult points off and bolting the folding wings in place doesn't change performance much ( unless one can find a performance report for the hundreds if not over 1000 Goodyear aircraft that were made that way).
We have been over the grab the B-26 engines and shove them in a fighter thing before. You wind up spending millions of dollars on a fighter that will be second rate by the beginning of 1943. And do you delay the P-47? The Turbo system is too big to back fit into a fighter designed without it and a fighter designed to fit the turbo system but not fitted with it is an over sized/over weight turkey.
The early R-2800s offer 1500hp at 14,000ft from a 2270lb engine. Which doesn't offer anything much over a Merlin XX (Packard V-1650-1).
I'm not aware that anybody actually tried that in the USA, hence no discoveries of the reasons for not using any? As for 'why' - as an insurance if the future turbo-equipped aircraft develop issues that might hamper timely introduction in service, while offering the performance punch similar to those? Should be quite simpler to produce and maintain, and cheaper than future P-38 with pair of turbos per aircraft.
There were a few commercial aircraft with push-pull nacelles in the early 30s. The Airacuda's used pushers with extension shafts. one of the drawings for an initial P-38 design was a push pull and another used buried engines in the fuselage with extension shafts/gear boxes in the wings and pusher props. how much actual engineer work was done on these I don't know.
the use of "push-pull" does nothing for the altitude rating of the engines involved. So a push-pull offers little altitude performance over a conventional twin using the "same" engines.