This really is beginning to sound like an impossible task unless you have intervention from alien space bats or
some sort of time traveler with foresight.
While the Beaufighter was called a fighter, it was slow. It used the wings of a slow torpedo bomber, and had assymetrical(sic) machine guns in the wings which slewed the aim when fired. The torpedo bomber had a landing light on one side and it was way too much trouble to remove and relocate. Fuel tanks were wisely installed instead of the guns, to increase range.
This might be seen as similar to adopting the Douglas A-20 to the task with a bit more redesign for the A-20 than in our timeline.
The Gloster F9/37 had a wing which was similar to the Beau, in that it was thick as a brick. Thirty mph slower than the Whirlwind on Peregrine engines, it only achieved it's speed by having a very tight fuselage, which would be destroyed by outfitting a conventional armament package underbelly. Over-the-nose visibility was superb, since there was nothing in front of the pilot, and I believe it might have made a good tank destroyer if armored and fitted with a Molins, underbelly. It would never make a fighter with wings that thick.
So the hero
The Foresight War would require a large bit of foresight to make it practical.
I did realize that the range on the Spitfire and Hurricane could be increased by adding additional fuel, but the only place to put it was where they put the guns, per PR Spits, which had lovely range. But then, they weren't fighters. Spits with 90gal drop tanks used to blow a lot of tires.
I imagine that they would have also handled poorly. The Mustang, a more advanced design, was supposed to be tricky with full tanks.
The twin-engine Supermarines were paper designs with vastly over-estimated performance figures, drawn up by a designer who didn't achieve fame for any original designs. Many of the technical specifications are unknown since the designs don't seem to be serious proposals. If they were, they wouldn't have made drawings where the cannons fire through the propellors.
The look nice. Still, Supermarine/Vickers was strained enough trying to improve the Spitfire particularly after the FW-190 owned the earlier Marks. So had they been produced, they not only would not have lived up to claims, they would have hindered the Spitfire program, allowing the FW-190 to maintain its dominance over the RAF even longer.
I love Hornets too, which is why my proposals #1&3 are a Whirlwind and a Welkin with Hornet wings. I've also drawn a twin-jet Hornet, because I'm capricious.
Of course, the Hornet is a wonderful aircraft. The problem is that it required years of experience with the Mosquito and years development to reach to reach fruition.
Turning everything into a Torpedo bomber was the navy's fault. Aircraft development takes a while, and while they're waiting, they like adding options. The mighty Firebrand and the homely Sturgeon, both flawed designs anyway, suffered further indignities by trying to do everything in one.
The Sturgeon was the greatest UK target tug of 1946 or so.
Doesn't anyone like Barnes Wallis' Vickers 432? It has the grooviest wing planform.
For wretched airplanes, the Vickers 432 rivaled Westland's attempt to do something with the dead end that was the Whirlwind, aka the Welkin. It is hard to say which was more egregious as both the Vickers 432 and the Westland Welkin were so awful. The Vickers 432 was so awful that it gives one pause to consider whether Wallis' stratosphere bomber would have been a total boondoggle if pursued.
Not that the UK was alone in having issues in creating twin engine fighters. My favorite example of failure, a plane that belongs up there in the pantheon of bad design--if not above--with the Welkin and the 432, was the
Bell YFM-1. This plane was weirdness with wings. Apparently,
the YFM1 was a horror according to test pilot Eric Schilling.
Of course, to offset this, the US also had the success that was the P-38. Despite being designed as an interceptor, the P-38 was able to fulfill a number of roles quite effectively.
The Germans had the Me-110, but this was sort of a mixed blessing. It really was not a classic fighter, as the P-38 was, but more of a bomber destroyer. The FW 187 seems closer but it may have had the issues of an overly small fuselage that would limit development, as did the Whirlwind.
The problem is with all the attempts at twin engined fighters is that no one was really certain as to what they wanted in a twin engined fighter. Fortunately, for Lockheed, the P-38 was a superbly versatile airframe that was able to move beyond the role of interceptor.