If you have a constant clearance between the pinion and rack, the rack would have to bend a lot more at the ends. This would require more force which your springs would not provide, so your backlash (or at least preload - the load below which your pinion would stay fully engaged with the rack) would change with position. Why don't you spring load the pinion against the rack as most designs do?
CNC mill build thread: http://www.cnczone.com/forums/vertical_mill_lathe_project_log/110305-gantry_mill.html