No, I am on the same page on the big JBL's. Listened to L300's a lot back in the day. Owned four L200's in a 4 channel setup. Almost put a pair of JBL 4350's on layaway at the old Audio Club for around 1,100 a pair. Missed a pair of L300's for a grand back before internet markets. Stories, I got a few.
I will politely disagree on the sound as I know the "New England" polite refined AR, KLH type and the "West Coast" JBL, Altec with the poster boy being JBL's. I know some of the sins of the big JBL's and the 300 can be a little forward and bright. Not too knock em as I love big JBL's and miss them and can certainly understand you never wanting to sell them. You would have to spend stupid money in today's dollars to come even close to the efficiency and dynamics of the big JBL's and for rock music I would argue you almost cannot find a more "accurate" reproducer.
In any event I am not the best poster for you in that I do not and have never run balanced. I think your Nak amps were designed by Nelson Pass and not sure how much it would help to go Mac. I really really enjoy some SACD's and have never heard an Ayre spinner. I know the rep of the Ayre and enjoy sacd and think it might give you a cleaner and nicer presentation hence my two cents with the post.
In any event, good luck and I hope you find what your after with your system.