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The Ta 152H doesn't even get to 4,000 feet per minute at gross weight.
No way it will outclimb a Spitfire. Fast? ... Yes. A great climber? ... No. Pretty good, but nothing unusual about it's climbing ability.
The Grumman F7F Tigercat, although it just made WWII, didn't engage in combat but qualifies as a WWII aircfraft by virtue of service date. I'd nominate the Grumman F7F as the best climber to 40,000 feet. But I would not be surprised to find a Grumman Bearcat and Supermarine Spitfire right in the same neighborhood, along with a variant of the Bf 109.
Few airplanes beyond rockets could climb with a 109, specifically the late model G's with AS engines, or the K of course. Might run out of fuel before 40000' though...
I haven't found the production P-51H Ceiling Tests but the XP-51G made 20,000 feet in 3.2 minutes, and 30,000 feet under nine minutes. The sustained climb rate of 2160 fpm available at 30K, and attained a ceiling of 46,000 feet - limited by lack of cabin pressure.
I suspect the Mark XIV will get there faster than a P-51H
Maybe go with the P-47M? Though I guess that Griffon Spitfires would've been 1st pick here.
Id love to know how the CAC CA15 compares to these figures. Powered by a griffon, max ceiling 39000'. initial climb about 5200fpm. max level speed of 447 mph, though one source claims that for a speed trial it once hit 502 mph in level flight (if that was true, its easily the fastest piston engine aircraft that I know of). but I don't have time to heights