One alternative history story I wrote had to do with drop-tank equipped single-seat Me 410's escorting Ju 390's and He 274's over Washington, Philedelphia, and New York. In my scenario, the Reich had captured Spain, Portugal, the Azores, and Bermuda. Fanciful stuff, of course. But when we start going down the what-if pathway all kinds of interesting things can happen. I do think the Me 410 could have cleaned up better than it did. If Germany hadn't been so battered in the air by the time it arrived, it may have contributed more in many roles. It was a true multi-role aircraft, much like the P-38 or Mosquito in that regard, and could have been developed even better.
Why would an Me 410 conceivably be selected to escort anything against the US from Bermuda? (it absolutely could not get halfway across the Atlantic from Spain/Azores). I haven't read your operational scenario but why do we think that it would not be even worse for the 410 against the P-38/P-47/F4U/F6F/P-51 ?? over the US? FW 190 would be far better choice of escort and how do you supply Bermuda unless you have totally annihilated USN and all land based USAAF bombers, USN torpedo and dive bombers?
One other note, in regards to the rear gunner. Robert Johnson, in his book "Thunderbolt", tells the account of attacking an Me 410. I don't recall the outcome of the encounter, whether he killed it or not, (don't have the book here), but I recall him saying he pressed right in there aggressively to down it, but was met by a stream of rounds from the rear gunner, whom Johnson admitted he had forgotten about. From that encounter it seems that the 410 rear gunner was sometimes underestimated in the heat of the moment, but not to be ignored.