I am on a mission to stiffen my Shapeoko 2. I have reinforced just about everything you can on the X and Y axis. Now I am trying to stiffen the gantry. While looking to see what all I could stiffen, I noticed most of my flex is from the v wheels/bearings themselves. Movement of the router up and down from the wheels on the X axis; side to side from the wheels on the z. I have them as tight on the rails as can be while still being able to move. But there is a lot of side to side play.
The V-wheels shouldn’t deflect appreciably under normal cutting loads — have you dismantled them and checked the bearings, the precision washer and the dimensions of the races?
Tim Foreman actually purchased a bunch of spacers and measured all of the parts so as to ensure that each wheel was the same dimension from the plate as all the others, with a washer matched up in dimension to the inner guide on the wheel.
If you can adjust your wheels properly, it doesn’t flex that much. Also check to see if V-Wheel bearings are clicking when you do that. I suggest to remove washer inside between two bearings and use thinner washer. Another idea is you can add one more V-Wheel for each side between existing ones by making same holes as originals.
Another thing to do is to switch over to through bolts for the axles as alluded to by @PhilJohnson — probably tricky to manage on the single piece X-Carve carriage, but worth doing if you can — it helped my Shapeoko 1 a great deal when I switched to a double-X-axis.