Giant 20' x 3' x 2' router build

[JAZZCNC]

Charlie I think mentioned before that you needed diagonal bracing on the lower frame and this would help your problem quite a bit but really your easiest option is the wall.
Personally I would brace the base along its length like the black line show and try it, but at same time a few brackets to wall would cure it easy. Then if you ever need it free standing then make some triangle supports (red lines) for it which go at the rear and bolt to floor.

Also becareful with those timing belts that you don't over tighten and pull the ends of the ballscrews inwards and cause them to bend or bind. The belts don't need to be drum tight just not loose.