Personally, I never understood why bother with wax for keeping the glaze off from the bottom.
How many seconds it takes you to wipe off the glaze from the bottom of a vessel with a firm moist sponge?
Problem with most waxes is that if this stuff gets anywhere else on your piece, you need to bisque fire it again.
Peel off stuff will mess up your brush and stink really bad. Just not worth the money nor the effort.
Keep your kiln shelves coated with kiln wash and use clean moist sponge to wipe off the glaze in seconds
BTW. Some pots, with lids, got glazed few days ago. All I used was watery mix of kiln wash between the lid and the pot. looks like it worked fine.
Glazed the lids and pots, wiped the edges clean with a clean sponge (keep the sponge clean!), added few brush strokes of watered down kiln wash and that was it.
I do agree with you, regarding the bottoms of projects, to an extent. I really depends on the clay body. For my first several years teaching, I used a low fire clay. Wiping those clean, wasn't too bad. But when I started at my new district, I used a stoneware. Wiping the glaze off of those, tore the sponges up something terrible. Using wax, was a much better option, considering I would have gone through quite a few sponges, with all the students wiping things off.
Dripping the wax was always a concern, and one I warned the students about. I also warned them about not getting it on their clothes either. Latex resist avoids the issue, of unwanted drips, since you can just peel it off.
A trick I saw somewhere and my local pottery studio uses -- found on CAD, if I remember correctly! -- is to get a piece of low-pile carpet, soak it in water, shake off the excess and lay it in a tray of some sort. Put the piece down on the wet carpet, press lightly, and rotate. Clean bottom and no shredded sponges or waxy mess!
(And yes, I know this isn't in regard to the lidded box, but don't think of it as a hijack. Think of it as... "the scenic route.")
The foam that comes in the cone boxes works too. I get that wet then put it on a wad of newspapers so the counter doesn't get soaked. Iron glazes on white clay I still use wax for, avoids staining the clay. Scenic routes are usually more interesting aren't they? Min