If the front edges are slightly short, the rocking you're experiencing is almost certainly due to racking, wich is the shelf twisting laterally under load. The cleats handle vertical load, but they don't resist side-to-side movement unless they are nailed into opposing pieces of structure. Since you don't want to disassemble it, the fastest fix is to add shear bracing. You don't need to perfectly correct the height mismatch; you just need to tie the structure togehter so the pieces can't parallelogram.
Get a thin strip of plywood or even some rigid MDF. Measure the inside corners where the tall side pieces meet the top and bottom pieces. Cut these strips to span diagonally from the inside corner of the top piece down to the inside corner of the bottom piece on the same side. These are just simple corner braces, and they stiffen the frame immensely. You want these strips to act like triangles, because triangles are what prevent rectangular frames from collapsing into a parallelogram shape.
If you want a more robust solution, expecially since it's holding heavy books, you can add a fixed back panel. Use thin 1/4 inch plywood for the entire back. Nail or screw this panel directly into the back edges of all your shelves and the side panels. This is classic cabinet construction; the back panel turns a fragile box into a rigid structure and instantly takes up all that torsional stress you're seeing. It will hide any minor dimensional issues from the front.
Applying the corner braces first is the easiest, fastest patch job. The back panel, though, is the profesional way to stop the wobble completely, and it makes the unit look finished. You can usually find good, cheap plywood sheets at any hardware store and cut them yourself.