Hey coco...
you're right in wanting to keep heat in the firebox, but I'm not sure that glueing tiles in the lid and upper part of the firebox is a good idea.
That makes me thing of the glued tiles of foam on the spaceshuttle.....
But seriously though, you do want some radiant heat bleeding off your firebox. Otherwise it would be extraordinarily hard to maintain a sufficiently (decently) low temp to smoke your food. An insulated box like that would be running pretty dang hot.
A better idea is to insulate the bottom for two reasons-
1) Saves the bottom metal of your firebox from heatrust and paint flaking.
2) Reflects heat back up to your fire and thus then into your smoking chamber. Maintains even firebox temperature...which is what we all want!
The arc of the SnP and similar models's firecox is a tough one, since it's hard to find true firebrick thin enough and of the shape needed.
We have to make do. I figured out a solution here this weekend. Found 2x2x8 bricks at Lowes for 38 cents each. They fit perfectly into a Snp Firebox and three insulate most of the arc well without sacrificing too much of your air space. For example, here is a shot of my firebox with the bricks in it. I have a 4 1/2 inch clearance from the firebasket to the bottom of the chamber, so it is a 2 inch sacrifice of space with these bricks:
Of course, you need a firebasket similar to my design, as the stock grate is only 2 inches off the chamber bottom.
From an overhead view, these bricks are just the right length to butt up against eachother, and with 6 of 'em you have a nice "floor" of insulation for cold weather or heat maintenance. Course in Kissimmee Florida no reason for all of this, but you asked!
Hope this helps with your mods and good luck to you!