[Galadriel55]

My take on that is that, as you say, this twain was an exception to just about everything - including how Elves are re-imbodied in Aman. I don't think that this is an assumption we can make here. Beren is mortal, and as such the rules for however Elves reincarnate really don't apply to him. Whichever way his body gets remade, it is not by the previous template. So why would it have to be in Aman? As for Luthien, she too is re-made as a mortal. This again defies the previous template. There is no precedent. Normal rules don't apply. So I don't think this is a valid assumption.

Regarding being in the earth for 3 years... Is there any indication in canon to say whether their "old" bodies still remained wherever they were entombed, or if it was literally the same bodies re-inhabited? I can only think of a fanfic, where the difficulty is resolved by them being buried in a crypt (rather than literally under the earth), and their bodies remaining unnaturally "fresh" - no direct explanation is made for that, but presumably because of them (or at lease Beren) being suspended in an in-between state of neither living nor yet truly gone.

A further question that arises if they arrived by ship is where did they land, and where did they go. Did they truly steer and dock a ship by themselves, with no seafaring abilities (but a pinch of divine intervention?), in a harbour where no one would take note, and make their way across Beleriand into Doriath, where again they pass through the country unnoticed just to surprise Thingol and the other inhabitants of Menegroth? None of this is impossible, but if you are gonna take the "reborn in Aman" angle, it needs a few further developments.