Every now and then I get a piece that has a drawer or drawers pushed in too far. It is annoying and looks sloppy. I am quite sure I did not "invent" this technique, but like to think I did:)
What I do is get a little chuck of wood, put a strip of wood glue on it and set it where you think is close the back of the drawer where it ends, but pushed a little forward so the drawer is sure to hit.
Slide drawer in and slowly push into place, carefully remove the drawer and add a clamp. You may want to recheck after you clamp just to be sure of your placement.
I always add a nail or two with my nail gun but I am pretty sure if you do not have that option, the wood glue will probably do just fine.