Tough call.
Had the Manix 2 XL since 2013, used it as my work knife since then. Has only the
tiniest bit of side to side play if I really try hard to find it.
A fitter at work liked my XL so much he got one, and that one has a little more side to side play, but not too much.
IMO the XL definitely needs the deep carry clip, carries so much better and there's a bit more there to grip with the fingers to make one handed closing easy. Love my XL, the ergos and full liners give a feeling of secure grip and strength that's completely confidence inspiring. Having the large XL in pocket is fine for me.
I'm real pleased with the CR, gotta love the Axis lock, and the thing is so easy to carry. Aesthetically awesome too, I haven't used it anywhere near as much as the others, but it seems durable.
As pointed out, it's not slicey like the other 2.
I'm hoping BM realize they need to make the midi CR now, 3 3/4" like the Buck 110. That would hit the CR series out of the park for me.
I'm a tip up guy, but I have no prob adjusting to carrying the Military. Easiest to carry of the 3 I think. Liner lock is so well done on the Millie too, though I prefer the CBL or Axis. And you're specifying S110V.
I'll say tip up Military with contoured scales and S90V is pretty awesome

though I guess that's out of your parameters.
Having spent too much time pondering this, I have now concluded the answer is - all 3. Pic to show it happened.
Ok, if it has to be only one for general EDC, I'd go Military, for the highly utilitarian nature of it and the edge holding of S110V.