This might give you some ideas:
To avoid backlash, the pinion will need some radial pre-load so it engages both sides of the teeth. The weight of the LR3 is one way to achieve this.
The issue that I see (apart from dirt) is that the rack/pinion is doing multiple duties in supporting loads in Z and Y and torsion in the Y/Z plane, while also driving the Y axis. If any pinion is slightly eccentric for example then it will translate into inconsistent Z height, or inconsistent Y/Z tilt. And I’m not sure what to expect as far as stiffness in the radial/vertical direction.
There is also the question of how you plan to constrain the X axis, if you are not using the tube on the right side.
I think it is safer to keep the motion separated from the drive, so the rack acts like the belt to drive the Y axis but not a kinematic support for other axes at the same time.