I can answer the question. The F8F was not the result of any USN specifications, rather its specifications, Design 58, were drawn up by Leroy Grumman, himself, in July 1943, just as the F6F was entering combat - and yes, it was influenced to a degree by the FW 190 and, perhaps surprisingly, also by the GeeBee racers. Grumman pitched the F8F to BuAer as a replacement for the FM-2s operating off CVEs; the word Grumman actually used was "converted," which, of course, meant CVE-type carriers. From hence comes the thought that the F8F was designed for use on CVEs. This was, however, a simple marketing ploy to get BuAer's attention. Grumman knew that in meeting HIS spec's he had probably one of the hottest, most maneuverable, and, certainly one of the fastest climbing, piston fighters ever to come off the drawing board. The Grumman concept presented to BuAer a fighter with the potential for a better power-to-weight ratio than either of the then serving F6F-3 or F4U-1 - ultimately, the production F8F-1 would exceed the 8,500-pound limit set by Grumman, rising to 9,430 pounds. It would exhibit, nonetheless, a power-to-weight improvement 25% better than the F6F-3 and 27% better than the F4U-1, not to mention 10% better than the FW 190 - he was banking on BuAer drawing the same conclusion and seeing the F8F as the replacement for the F6F. And evidently they did, telling Grumman not to worry about the CVEs as they wanted the design for the new CVB class carriers as well as CVs. The flip side would have been that if BuAer decided it was only interested in replacing the FM-2s, then here was the absolutely perfect replacement designed to exactly that. No, the Navy was so impressed with the design that by November 1943 BuAer had authorized construction of two XF8F-1s and thinking about how to get them to the CVs.
So, the plan was developed to gradually eliminate F6Fs and replace them with F8Fs; push the F6Fs down to the CVE VC Rons and make them all F6Fs in complement, discarding their TBMs as they had no torpedo targets anyway and the IJN submarine fleet was seen as of little consequence (perhaps a somewhat premature conclusion). The thought was that there were sufficient F6Fs constructed already or in the pipeline to outfit the CVEs so that Grumman could concentrate on F8F production. There were even contracts for Eastern to build F3M's, the Eastern F8F, under license and discontinue FM-2 production. Eventually F8F production would catch up and the venerable F6F's, probably reaching the ends of their true combat usefullness aboard the CVEs would be replaced by F8Fs. And Leroy Grumman's originally pitched plan would finally come about. But not until the F8F was firmly in place on the CVs and CVLs. Note there were a total of 5253 F8F-1s plus the 1876 F3M-1s (total 7129) in those F8F contracts that were OBE and canceled; more than enough to fill both combat and training requirements for the plan.
Now, why replace the F6F with the F8F instead replacing the F4U? While acknowledged as a excellent fighter,the F4U was equally valued as a strike fighter, that is it's ability to haul and deliver ordnance. And, yes, so could the F6F, but if the F4U were eliminated, that presents the problem of Grumman having to producing both the F6F and the F8F, not to mention the F7F. It was not that the Navy was unhappy with the F6F, it was simply an economic/production issue. So, the F6F got the chop. Probably, IMO, much to Leroy Grumman's relief for, as with the F4F when it was replaced by the F6F, there was really not much more that could be done to improve the design.
Actually, this fell right in line with the Navy's thinking on fighters in the latter 1940's and into the 1950's. What BuAer wanted on carriers was a fast moving, fast climbing fighter for fleet and point defense and a second fighter for long range interception with a heavy strike capability. The F8F/F4U team fit this bill perfectly. After the war we see the same pattern; in fact, it was the F4U that was the type that stayed in service. So also, perhaps BuAer's enthusiasm for the F8F was also a hedge on the potential operability of jets (remember the FD-1 was also authorized in mid-1943). In the end, overtaken by the end of the war and technological advances, F8Fs were replaced by jets (F2Hs and F9Fs, mostly) and F4Us remained the duty fighter-bomber type as it was a better ordnance deliverer than the smaller F8F.
If you look at Navy planning documents written in late 1945 for naval aviation organization in the post war years the first thing that jumps out at you is that by December 1945, the plans show CV's with four possible air group configurations:
A - 49 F8F; 4 F8F-P; 4 F8F-N; 24 SB2C; 20 TBM
B - 49 F4U; 4 F4U-P; 4 F4U-N; 24 SB2C; 20 TBM
C - 31 F8F; 2 F8F-P; 4 F8F-N; 36 F4U; 15 SB2C; 15 TBM
D - 25 F8F; 4 F8F-P; 4 F8F-N; 24 F4U; 12 SB2C; 20 TBM
CVL air groups were specified to have complements of 22 F8F; 2 F8F-P; 9 TBM.
CVE air groups were specified to have complements of 16 F8F; 2 F8F-P; 12 TBM.
CVG(N) were specified to have complements of 1 F8F-P; 36 F8F-N; 18 TBM.
The only place you see F6Fs mentioned is their possible use as nightfighter and photo-recon types until the newer F8F and F4U types for the same missions become available.
The F8Fs bread and butter was the rapid climb to altitude as a fleet defense fighter. With an R2800 engine on such a, comparatively, light frame the F8F was capable of some remarkable performance. Indeed, on one occasion, at the Cleveland Air Races in November 1946, a couple of F8Fs performed back-to-back climb to times, from a dead stop to 10,000 feet, the first in 100 seconds and then, the second, 97.8 seconds. The 97.8 second record, including a 115 foot takeoff run, was a record for piston aircraft that stood for many years and, I believe, still stands for standard equipped military piston aircraft.
Rich