Looking back on your idea, you might have issues keeping all the veneered parts perfectly aligned and "project ready" if you intend to pre-cut everything. The veneers like to slide around a bit as things get clamped.
A way less stressful approach would be to just make a full-front sized panel, then use a thin kerf blade to cut things out. Your drawer gaps will probably be equal to the blade kerf anyway. I have an 8" circular saw blade that has a 1/16" kerf and fits my table saw. I use that all the time for fronts. Perfect with a 1/16" kerf between drawers for clearance.
Depending on the veneer, you may want to lay a strip of masking or blue tape along the cut lines to stop chipping.
Not really an issue on the top side, but the back side can get "rough", especially on cross cuts.