[mst]

I honestly don't know if the play in the mechanics could affect the centering quality (due to wobbling of the whole tube). In the two cases where I had that kind of play, I sent the lenses to Zeiss and their analysis and cost estimate mentioned the play and centering issues in both cases.

Also, in both cases, parts were replaced to fix the play. So, even if you manage to successfully open and reassemble the lens, I'm not sure there's much you could do about the play yourself without replacing parts. Also, in addition to all the warnings from Toni: some lenses feature unexpected surprises for those fearless enough to just grab the necessary tools and exploring disassembly. Like, spring loaded screws, bolts or shim rings, for example, usually way too small to ever find them again after their ballistic flight across the whole room... I learned myself the hard way

Since you mention the softness is equal across the whole frame, I guess the best approach now is to check the lens on a digital camera, preferably one with live view, as Toni already suggested. That should give you a good idea if the softness is a general issue of the lens or a result of front or back focus.

Practically all ZM lenses (with the exception of the 50/1.5 maybe) are great performers, so you should not see noticeable softness in any case, especially not on film.