Fitting a square into a parallelagram is not going to work. The easiest may be cutting a tapered board to fasten to the front of the drawer and then...
Some polyurethanes will be too soft and not polish well. There is a distinct difference between dry and cured. Cured when the temperatures are cooler...
Cut a piece of wood to fill the gap and just wedge it in. Second option is to raise it up so she can't see behind it. You don't want kids ringing it...