I have not played the 'new design' LM's, so can't really comment specifically.
To the OP, I guess I have played my share of very heavy (12+ pound) J basses, and you couldn't pay me to play a bass that heavy again.... ever. Body weight will result in a somewhat different tone, but different is not necessarily better.
I guess if your goal is to mimic a true 1977 (or whatever) J Bass (most of which weighed a ton), then the newer models using the heavy northern ash would be the way to go. The slight difference in the headstock and slightly wider body seem minor to me. If, on the other hand, you want a bass that gets you into what most would call a 70's type tone in a 9 pound or so format, the 'older stock' lighter weight ash would be the way to go.
Just realize what you are getting into if you go '70's weight spec'. I find that completely brutal on a 4 hour gig (I had a Celinder update that was over 12 pounds), and again, the slightly more aggressive, less sweet tone of most of the heavy bodied J's I've played is not necessarily a move in a 'better direction'.
There are clips on my youtube channel that are very representative of the tone of my older spec lightweight LM, so maybe that will help you decide one way or the other. Pure personal opinion... again depends what you want. I have yet to play an A-C that didn't sound great in its own way... hard to make a mistake, other than to get a bass that is so heavy that you don't want to play it on a gig!
On my scale (which is not a professional scale and may be off somewhat) my LM5 is 10 pounds. Considered a medium weighted bass. The heavier will sound slightly different if you a/b it as you said. In fact everything you said i agree. Jimmy once said the heavier (not word for word) will give a darker sound but not meaning darker as bad. When people say darker some believe you will get no snap whats so ever. But warmer may be closer to what its meant. I notice the lighter give more of a bark to it. As you get heavier ( as with mine) I get a warmer punch to it. But again a nice slap also which are very signature to the 70's maple neck fenders. I had a 73 P bass i had bought from someone who thought it was too heavy. To this day I blame that bass for my left shoulder tilting down
The 10 LM is fine. But again the heavier will give it different tone possiblities. My Sadowsky I have to check the gig bag to see if the bass is in there. Very light and very brite. SVTBass did a nice recording on it and it sounded very good and bright. Somewhat brighter than my AC. I have not played it much as of late. I did a recording with the AC recently and the engineer was amazed. For me it fits. The person who is considering a heavier bass may keep in mind the differences. But I am not sure because Jimmy is making them wider will also make it that much of a weight difference. It may not make a difference at all. Man I need a LG5.

...sorry...