Hmm...I don't recall seeing any documentation giving 6000fpm climb rate.
Here's published figures for War Emergency Power: http://www.wwiiaircraftperformance.org/f7f/F7F-1_Airplane_Characteristics_Performance.pdf
They list 4360fpm with 426 gallons of fuel onboard.
I doubt a 51 gallon decrease in fuel load would produce 1640fpm increase in climbrate.
That figure is for the XF7F-1. Further down in the document is the climb chart for the F7F-1, which attained 4,250 fpm in MIL power (the production aircraft had a newer, high activity prop). In October 1945, the Navy did a test with an F7F-3. From a standing start, the aircraft reached 10,000 feet in 104 seconds. That's an average of 5,769 fpm, including the takeoff roll. An F8F-1 was also tested the same way (in 1946). From a standing start, it reached 10,000 ft in 96 seconds. This record stood unbeaten until Rare Bear edged it out (91.9 seconds, IIRC). That's averaging 6,250 fpm (including the takeoff roll). Like the F7F-3, this was an unmodified F8F-1, carrying ballast equal to the weight of MG ammo.