You are betting on an under armed, unprotected plane to outmaneuver and out performe the Zero and Ki 43 while using an engine that is, at best, no more powerful. That big wing is actually smaller than the Japanese wings, although not by much. No combat flap to match the Ki 43,either.
Armament is problematic. Even if supplied with Italian guns the ammo supply is not going to continue after the summer of 1940. British .5in ammo is close and might even work with minor modifications to the guns but the British never issued a .5in HE round. British might be faced with fitting US .50 cal guns for somewhat common ammo supply. Dropping to a pair of .303 guns is probably not going to happen.
Without redesigning/ rebuilding the wings mounting guns in the wing is out. The wing was the fuel tank. You not only have to seal up the space the guns and ammo would take up but route firing controls and possibly gun heating systems through the fuel space?
Anything can be done if you throw enough effort and money at it but this does not look like a good option.
BTW, the engine doesn't look good either.
I think viability of the Re-2000 hinges on a new engine. An Re-2000 with a R-1830 (or some British equivalent) and a pair of M2 browning nose guns looks pretty good to me, probably as good as a P-36. Especially if you put an armor plate behind the pilot. If you can manage self-sealing tanks obviously much better, then you are starting to put together a first line fighter I think. Two M2s is enough to wreck most Japanese planes of the era including bombers.
With a Merlin or an Allison even more so.