I would not remove Death Star II. It’s iconic, it’s something that’s a big part of Star Wars, like it or not. I mean, it’s even the logo for this website.
Yes, I agree it’s more iconic than DS I due to its more interesting design, but I can easily think of it as DS I while still under construction.
As a general rule, I wouldn’t remove things people expect to see when they watch a certain Star Wars movie. That includes major characters, settings and plot points. Like, if it would be on the poster of the movie, leave it. Jar Jar, ewoks, DSII, Star Killer Base, etc.
You know I usually apply the same philosophy to my edits; I don’t change things that would cause major discrepancies with canon. I think a good rule of thumb is “Is it in Lego Star Wars: The Complete Saga?” No one talks in that game, so you can get away with changing small informed plot points, but the rest is pretty clear. My edits should function as replacements to the originals, so you should be able to discuss the film having only seen the edits…to an extent. That said, I make exceptions for things I find just too monumentally stupid to include, continuity be damned. The only elements that are that bad are Leia being Luke’s sister (universe-shrinking) and additional Death Stars. Oh and I did remove Anakin building C-3PO, but I wouldn’t consider that nearly as big of a sin (even though in theory it should be as bad as Leia Skywalker). It’s just kinda pointless.
Anyway, back on topic, what I do with Starkiller Base is just make it a base. Not some superweapon, just a base. If they really wanted it to be a superweapon they should’ve at least stuck with the original name Doomstar, which reflects its status as a beefed up Death Star, rather than Starkiller Base, which is a questionably placed nod to Luke’s original last name, functionality be damned. Oh and sure, it does literally kill stars, but then again star destroyers don’t literally destroy stars. I guess the problem for me is that I can’t not see it as a last name, and naming the base after someone just feels weird. Okay, well, there goes another tangent. Anyway, I think DS II has to go. The Emperor is aboard the Eclipse; end of story. That said, it’s kinda funny how this unintentionally makes TLJ retroactively more similar to RotJ (Snoke was aboard the Supremacy).