BTW, I love my Luxman integrated and the only amps I've heard better are the D'Agostinos.
My only reason for suggesting to keep your separate is the damn low mid-bass issue. It may be helped by a bigger amp with more current and output stages.
Since you already have the amp, I'm suggesting you keep it and get a matching pre, but listening is key, and honestly, when these issues come up they are NOT difficult to hear.
Listen with an integrated to something with significant bass, especially electric guitar or kick drums. Switch amps. Hear no difference? Buy what is cheaper, smaller and more convenient.
Does one amp magically sound more full and breaths easier? Buy that one.
Like I said, every time I've seen a speaker with an impedance curve like this they become very amp fussy. I have even seen speakers with this drop deliberately created to make the speaker seem more demanding. Like I need a Dominatrix for a speaker, but apparently many do, and prefer the speaker that will demand a beefier amp.