this kind of stuff hurts far less when you have not yet started building!. Your far better at sketchup than I!!!.. Im no expert but do you think the gantry beams (purple) may be a little thin? not that it matters I suppose because you can always add extra support if it does flex. As the two beams are on their side I should think they will be ok on the X plane, however applied pressure on Z while Y is in the middle may perhaps cause flex? Mind you it is only around 15" wide so it might be ok... what do you think?
when do you hope to start building?