Your question is a bit confused. Perhaps I didn't phrase my post properly.
Vought won a 1938 design competition for a replacement for the F4F. That is they way they did things in those days, they were working on the next generation aircraft as/before the present one was going into service. Vought gets a contract for the prototype XF4U-1 on June 11th 1938. This three years before the contract for the prototype F6F is placed, Vought got a production contract for 584 production planes on the same day that Grumman got the contract for the prototype F6Fs, not quite the same thing.
Only ONE F4U existed at the time the the contract was placed for the F6F prototypes, and it was a rather different aircraft than the production versions would be. Part of the reasons for the long delay in placing the production contract is that it took about 23 months from placing of the contract until first flight of the prototype. In about 13 days the plane is damaged in a forced landing and requires almost 3 months to rebuild. It is now October of 1940, the plane completes Navy testing at the end of Feb 1941. In March negotiations start on the production contract which is not finalized until June 30th.
During Navy testing it is found that some of the Navy "standard" tests do not apply to modern monoplane fighters or are dangerous to perform. The F4U pushed the boundaries of aerodynamic knowledge of the time just like the P-38 and ran into some of the same problems, like compressability. A standard Navy test was a vertical dive lasting 10,000ft. The Corsair was enough faster than previous fighters ( or dive bombers) that pulling out at 10,000ft didn't leave enough room without excessive "G" loadings. and starting higher than 20,000ft ran into problems with compressability. Another requirement was that the plane had to be recoverable after 10 full spins in either direction. Both requirements were changed for later aircraft.
Also remember that in 1938 when work started the R-2800 engine pretty much existed only on paper. P&W doesn't fly an R-2800 until the summer of 1939 in an Vultee A-19 and it is not the 2 stage version. How much waiting Vought had to do for the engine and propeller I don't know, maybe none, maybe a number of weeks.
Prototype F4U had been in existence (after first flight) for 6 months when the Navy makes the request for production versions to change armament, armor, fuel tankage location and changes to ailerons for better role response.
I would also note the world situation was rapidly getting worse during this whole time and the F4Us first year on the drawing board and mock up construction was in peace time for the whole world. The finalized contracts for the production F4Us and the prototype F6Fs were placed just a week or so after the Germans invade Russia and US -Japanese relations are getting steadily worse.
Grumman did a fantastic job with the F6F but there are a number of differences between it's design/development and the F4U's.
The F4U was found to have a strange stall characteristic in which one wing stalled before the other, and the landing gear shocks were too stiff causing excessive bouncing on landing. Since carrier planes land closer to the stall than land planes and usually land with a higher vertical velocity these are both problems for carrier use that are much less troublesome when used from a shore base.