Why am I getting demoted when I get 4th place?!

Because Riot is using the same dumb and shitty mmr system they use in Solo-Q to make unfair matches :)

Maybe you shouldn't be progressing as 4th past a certain Rank?

Makes sense, even in silver a 4th place win only gives less than 5 points. So by diamond it should be negative. Silver 2 you can get 19 for first place, -41 for 8th place. It's designed around the logic that "everyone belongs in iron, so even in silver we set it so the net points is heavily negative across the whole 8 players"

Not sure how it works, but could there be a chance you matched up w/ lower elo folks (golds maybe) so placing #4 lost you points?