There was some concern about my last rod deflection test (not shown here) so I ran it again in a more true to life setup. I used two rods and LM12LUU linear bearings along with a lead screw for good measure. I also mounted the test rig to a piece of plywood to ensure there was no flex.

The flex was greatly reduced and it appears more linear in nature. I think mounting the rig to a solid base provided the biggest improvement.
I can still get a lot of flex just by pulling on the top of the y carriage. I measured a full cm of motion at the top. I suspect a solid mount between the y carriages would help a lot with rigidity as well.