At a quick glance, it looks as if a fair bit of the loss of stiffness as you move out from the gantry towards the tool is actually coming from play or flexibility or otherwise in the Y and Z rails, plus a component from gantry twisting. Your first figure is presumably bending of the gantry, primarily, and then the other effects become larger as you move out from the gantry. Maybe the Z bearing spacing could be increased? Reduce thickness of Z moving plate to reduce leverage? Deeper gantry? I'm playing with ideas for my own design and just finished my first pass (on paper) at the whole Y/Z assembly so very interested to hear your thoughts. I think that by reducing clearances and cutting clearance grooves in moving and fixed Z plates you can just about fit a ballscrew nut in between while still using 15mm rails but it's all a trade-off, of course, as you are weakening the plates a little.
Thanks for giving the data - it's good to see real numbers to start to get a feel for what is happening in the structure.