Wow Nick! It looks like you hit the nail on the head basically as to what the issue is.
At first the Firewall didn't seem to like that exact format but online it said to try "-p tcp --tcp-flags SYN,ACK,FIN,RST ACK" but that still seemed to have the exact same issue.
Then out of curiosity I decided to comment out both the Up & Down ACKs just to see what happens.
All the sudden the PC doing the downloading seems to have properly moved to Priority 7 (Web)/Priority 6 in the command. Still tons of "dropped packets" but I guess like you said it's to have the server/sender slowdown.
The PC was downloading and the Fire TV Stick was watching content as expected without non-stop buffering.
All I can figure is the download maybe floods the ClearOS PC with so many 64-byte packets that it drove the QoS wild?