What am I supposed to use instead of cardboard for attic light dams?

You're looking for what the industry calls **insulation covers** or fire-rated recessed light enclosures. Your inspector is flagging the cardboard because it's a combustible material, and even if those LEDs run cool, the driver inside the junction box can still get hot enought to be a risk if somthing fails. Cardboard is basially just tinder sitting next to an electrical heat source, and no inspector is going to let that slide.

If your lights are already **IC Rated** (Insulation Contact), you technically don't need a dam at all because those housings are designed to be buried. But with loose-fill, keeping it back is still a good idea so you don't get a face full of cellulose every time you pull a trim down. Most guys use Tenmat covers or similar mineral wool domes. They're specifically designed to sit over the fixture and keep the insulation away while maintaining the fire rating of the ceiling. You can ussually find these in the electrical aisle, though sometimes they're tucked away by the insulation or drywall supplies. If the store is out of stock, another common fix is using aluminum flashing. You just cut a strip, roll it into a cylinder around the light, and staple it to the joists. It's cheap, non-combustible, and will pass inspection every time. Just avoid using random plastic tubs or buckets. Unless it's specifically rated for this use, it’s just another fire hazard. It’s a bit of a pain to crawl back into the attic and swap them out, but it’s the only way to get your permit signed off and ensure the house stays safe.

I acutally saw those Tenmat dome things at the big box store yesterday but I walked right past them becasue they felt like heavy felt. I didn't realize they were fire-rated! If I use the aluminum flashing instead, do I need to worry about leaving the top open? My attic gets pretty breezy with the soffit vents, and I'm worried the insulation will just drift right over the top of the cylinder and bury the light anyway. Is there a specific height I shoud aim for to keep it clear?

If you go the flashing route, make those cylinders tall enugh to clear your insulation depth by at least three or four inches. If drifting is a real concern, you can zip-tie a scrap piece of hardware cloth over the top. It keeps the cellulose out while still letting heat dissipate.

Honestly though, save yourself the headache and just grab the Tenmat covers. Fighting with sharp aluminum flashing in a cramped, dark attic is a recipe for sliced knuckles. The pre-made covers are a "one and done" fix that won't shift around when the wind kicks up through those soffits.

If you don't want to mess with rolling flashing, check the HVAC aisle for some 8 or 10-inch round metal ducting. You can just cut short sections of that with snips and it works the exact same way. It's way stiffer than the thin flashing and doesn't want to coil back up on you while you're trying to staple it down. Also, check your light boxes for the 'IC' stamp while you're up there. If they aren't rated for insulation contact, those Tenmat covers are realy your only safe bet to keep the heat from building up too much.