Curate, connect, and discover
The most hilarious thing about the fact Buckbeak had a trial and lost is that later on JKR resolves the issue by having Hagrid take him in again and renaming him Witherwings. That’s literally all it took. What if in POA, Hagrid simply said, “Sorry, Buckbeak flew away.”
“There’s a hippogriff right there, Hagrid.”
“A different hipprogriff.”
“I’m… pretty sure that’s the same hipprogriff.”
“Prove it.”