I'll weigh in as someone who does use heat plates and likes them: the exact temp under it doesn't matter as much (since they work differently than heat lights), the behavior of the chicks do.
Chicks that are under and sleeping quietly are happy warm chicks; chicks that are peeping a lot are too cold; chicks avoiding it are too hot. In general, you want the chicks to be able to comfortably touch their backs to it when laying down, while still having room to easily come out of every side to avoid suffocation if a bird can't escape the huddle. For new chicks, I place the heating plate in the middle of the bin to reduce the risk of them losing it, and listen closely after lights out the first night to make sure they're comfy. I also do a health check in the morning and randomly throughout the day where I lift it up for a head count.
Heat plates should NOT get hot enough to burn a chick, even in direct contact with them (since they're SUPPOSED to be in direct contact with it). Your plate is defective and should be returned or exchanged, which should hopefully be easy with the burned chick photos. I can't tell your brand from the picture, but I use Rent-a-Coop (with the anti-roost cone, save yourself endless poop scrubbing), if you need a brand rec.
Also yeah, as you realized, that was WAY too many chicks for a single heat plate. People doing big hatches typically use lights.
It sounds to me like there wasn't enough room and it was too hot, so some chicks left to huddle together, got too cold, and health issues spiraled from there. Hopefully the rest of the chicks are good from here!
But again: good heat plates DON'T burn chicks, the whole point is that they're LESS of a fire risk than lights, get a new one ASAP. Then do health checks and keep an ear out for any unhappy peeping.
Edit: Also make sure you're slanting it so there's a low side and a high side: this lets the chicks pick how warm they want to be and gives more wiggle room for your faster growers.