Don't think there is much you can do, but I wouldn't think vertical play is too much of a prob'. I think they all have some vertical play, you just don't normally notice 'cos it's fairly heavily spring load.
If you really wanted to take it out, I guess you'd have to make another shaft that engages on the rack cut into the quill (the shaft that has the operating lever(s) on the end of it) Or buy a new one... but I doubt a new on would be better.
It's the side play that's the killer and prevents accurate work.
I tried shimming out my cheapo one, it helped a tad but made it noisier. I bought a mini mill for more precise work, I've really enjoyed refurbishing that
Del