I am only going as deep as the plastic is thick, in the cutting action. I know enough not to nick any coolant passages. I'll take the piece and make a door out of it for easy access and complete cleaning.Sounds like you hate your truck too! Cutting a hole in your hvac case is not a very good idea.
Being that the mice got in on that side of the heater core to blow out the vents then you might also want to figure out where they are getting inside the truck at.
Do you think I want to go through removing the entire heater box to clean it every year? I have tried every which way to blow or vacuum the crap out. There are four diseases you can get from mouse droppings. Hantavirus is the one that will kill you.