I have found out what the common name of my crazy celosia plant is: cockscomb. Because the fuzzy, broad blooms
I've also seen ones for sale at the grocery store, that have the blooms snugged close against shorter plants (a foot and a half or so high) with large leaves like my tall ones. I'm guessing those were started early too, but then cut back so the flowers would be on stout, thicker stalks (and maybe not fall over).
Here's how the mailbox spot looked in late september, after I cut off the biggest cockscombs: