In TROS, the gang refer to the wreckage of the Second Death star on the Endor moon as simply ‘The Death Star’, presumably to not complicate things. I think that adds to the list of good reasons, not least of which being that under the ST in particular we have way too many Death Stars, that we should consider having the DS2 just be a part-repaired DS1.
In ANH, I’d edit the explosion to make it look more like massive damage than full destruction, and in ROTJ, I’d remove references to it being another DS, and add references to it being simply under repair.
I was working on a 3-in-1 fanedit of the OT that just had one Death Star (and one rebel base on Hoth).The 3-in-1 part didn’t pan out in a way I was satisfied with, but I’ve been thinking about reviving the project and giving it another go, or maybe trying a different format like a 6-part series.
There being two Death Stars has always been something that bothered me though and this makes it extra relevant.