My kids aren't allowed to get "froggy".
They know the rules and they know the consequences if they go getting amped up.
I don't allow screaming or loud noises. I have children 12 months and younger that require morning naps, we also do activities during the morning time, etc.
The decibel range is definitely a little higher after nap and after they wake up but that's to be expected. They know what time it is and they will soon go home.
Are their consequences for behavior or not following your rules?
It sounds to me like he needs to have his "goodbyes" with his parents before you open the door that way it's a hand off of the child and a "bye, see you this afternoon." Would that help with the noise you are talking about?
How about rather than looking in his angry eyes for 10 minutes, you redirect him and if he can't pull himself together after 60 seconds, he can go have a seat somewhere. Looking an angry child in the eye is looking a bull in the eyes. Who's going to win and is it really worth the fight...KWIM?!
As for the screaming at the gate...is there anyway to get a half-door made to block off the room? Maybe if he can't see in there, it wouldn't be an issue. How about keeping him away from the gate? Would that help?
Keep this in mind...the best way to redirect a child's attention is to physically take them to the farthest point of the room without saying a word. They will physically need to turn themselves around and it usually takes a few minutes for them to realize what happened, what they were doing, and how they got there. 90% of the time, they forget and go about something else.
Works like a charm here!