I would definitely never stack the totes- and the only kind of lid I would use would be a frame of hardware cloth which allows for lots of air and can help keep household pets from "playing" with your babies, and to keep babies that can jump in there, but only as single layers.
The issue with some of the heat lamp bulbs- and there are many, many issues with heat lamps in general, though of course they are widely used- back to the bulbs - some of them have a coating that emits a gas that kills chicks. I don't know which ones do and which ones don't but it can be devastating.
If the chicks were killing eachother (with the exception of a fear-huddle where they crush a couple of their flockmates) -- there would likely be blood. Once there's blood, that poor chick is doomed unless removed, and there would be plenty of tell-tale evidence.
Cedar shavings contain something that is lethal to baby chicks. So only pine shavings - or - in my humble opinion, compressed pine pellets that are sold in 40lb bags are best- sold in our area as "Nature's Bedding" or "Dry Den" - or paper towels. I like compressed pellets because they dry out the little baby poops really fast. The downside is clogged waterers unless you're using poultry nipples.
Personally I'm a big fan of the heat pad method (MHP) where you make them a cave using a heating pad that won't turn itself off after 2hrs-
Walmart carries them for around $14... and some kind of frame so they can go under it to warm up, and go out the rest of the time and play.
Chicks with a momma hen go out in all sorts of weather. When they're cold, they run back under her, press their little backs against her body, warm up, then they're off and exploring again.
As humans keeping these little babies in artificial environments, sticking as close to mother nature as possible tends to give the best results. Heat lamps suck up electricity and they make everything artificially hot when the chicks really only need a warm up area. Otherwise, think of it as being stuck in an airplane on a hot day when the pilot can't turn on the A/C for the passengers.
Things like coccidiosis thrive in those kinds of conditions. I'm not saying that's how yours died- but everything bad likes those warm humid conditions.
They still need to be kept out of drafts from your fan or air conditioner regardless - because that cold air flow will rob them of the heat- but all the same they need an environment that allows the high concentration of moist air that comes from their breathing- and it's a LOT of moisture they expel - to escape.
