Yeah, yikes! I forgot about the Goshawk. That definitely does illustrate the problem. Which in aggregate, does mean you needed not just a slimmer fuselage, but a redesigned wing with somewhere to put the main landing gear other than in the fuselage. Which means basically a whole new plane. A Hellcat, in other words.
The Corsair has a thinner fuselage (max width) than the Wildcat too I'm pretty sure, in spite of having a bigger engine with a wider diameter. So it's definitely doable.
Hellcat definitely looks sleeker than Wildcat, but it still has a bit of that Wildcat style beer barrel fuselage shape.
The disadvantage of the Corsair layout is poor forward visibility, the cockpit is far back because there's a big fuel tank ahead of the pilot, whereas the Hellcat pilot sits on top of the fuel tank.