If the doors are already glued, I'd be tempted to drill 1/16" holes
from the back into the bottom of the grooves holding the plywood
panels and use a caulking gun .........


This might work, and a Glue Syringe might be a better choice. Most come
with 3-4 different needles and the larger ones should work with silicone.
Just squirt the goo into the syringe from the tube and be careful not to
squeeze out around the panels. The resulting holes won't be any bigger than
a finish nail.


RonB