I own the Meze 109 pro and also heard all the Meze line up and a lot of the ZMF line up at London CanJam.
Here's my brief thoughts from that experience, and as ever, it's only my subjective thoughts.
In the Meze line up I instantly warmed to the 109 pro. Looks, comfort, but above all sound. Definitely coloured tuning but with good treble extension and a wide soundstage. I instantly fell in love with it. Moved onto the Liric and had the complete opposite. Horrible fit, wasn't keen on the looks but above all the tuning wasn't to my liking either. Instant flop for me. I then tried the Elite. Wow!.... Just Wow on every level for me! Above anything else I tried that day the Elite gave me the most realistic instrument placement and timbre I'd heard. On anything I threw at, which included Classical, Jazz and all sorts in-between, it just shone! My end game headphone for sure. I came back to the Empyrean at the end of the day. Tbf it had been a long day and at that point it just felt like the little brother/sister of the Elite. Very nice but not on Elite level.
The first thing I heard of ZMF was what is now being called Bokeh (hadn't been given a name at that point). I absolutely loved it instantly!, on every level. The best closed back I'd heard that day by a country mile. I then tried the VC. Again, very very nice but I preferred the tuning of the Bokeh just a bit more. I then had a line up of various other models laid out for me from the lovely people at ZMF and tbh I can't remember all the ones I heard, and at that point I was most interested in closed backs as I simply could not believe how good the soundstage was on the Bokeh and VC. I never thought that was possible on closed backs. I think I heard the Verite open, but if I did it didn't stand out. I really liked all the half a dozen or more ZMF models I heard, but the winner for me was the Bokeh, and that was before knowing the prices.
When you say you want a very musical and absorbing experience, about 3 months into 109 pro ownership I'm getting that in spades. At the price point it's an absolute killer for me. Of all the ones you mention though the Elite stands out as truly special in every department. It perhaps wasn't the most 'exciting', in the same way as the 109 pro and Bokeh are, as it's just sooooo smooth and gorgeous on everything you throw at it, but I found I could enjoy it both for analytical listening and also for just kicking back with. I dream of one day being lucky enough to own a set.
Sorry for the ramble as it probably doesn't answer your specific question. Only you can really decide on comparisons from your own listening, and for that I can thoroughly recommend CanJam, if you can get a quiet space and/or get in early, which luckily I did with the Meze's and ZMF's.