Just make a fifth instance if you wanna design five fights so badly. There is a way to do door bosses right, and XIV has gotten it right all of twice--Exdeath and Grinny/Adelphel. "Right" in my mind meaning "a short appetizer of a fight; 2-5 minutes MAX preference toward 3 minutes."
As it stands, SE very consistently delivers 6-8 minute fights, nearly the length of full fledged savage floors of the same tier, that are brutal and have a full progression of their own. All for no reward save for "you can now fight the real guy, but with less time in the instance to do so."
Imo, they're not fun. They're annoying at best, stressful and aggravating at worst. The presence of the door boss actively makes both the door boss and real boss less fun for me, because they're tied together in one instance means I can't relish victory over one and I'm on a strict clock with the other.
I get the desire for spectacle. It was amazing when Neo appeared the first time; the cutscene that defined Stormblood raiding. Kefka transition was neat too, but by Omega it was expected. I enjoyed ShB quite a bit until 12s happened and we've had door bosses ever since.
Tl;dr: this is a request to cease with door bosses. If the desire is to make five fights, make five instances and redistribute gear accordingly. That, or at least restrict them to sub 5 minute affairs to prime us for the real fight.