Do a quick test buy moving you glass plate up on a box or something. See if your speeds can be increased that way, if not your middle assembly is too loose.
Let us know so we can start to put some firm size limits on this if we are reaching them. My z axis is 6″-8″ and my next build will be shorter. I have only printed 1 large item on my robo and that was 1 lamp shade, other than that biggest things I print are the roller f’s.