I've only seen like the first two episodes of the original and all of BH. I didn't feel like the opening was rushed.
The rushed feeling might be because the original was slower, so you compare it to that.
"The FMA animation was created before the manga was finished, so the animators had to create their own story once they crossed a certain point since they weren't privy to how the manga's story would conclude."
And this is why anime shouldn't be created until the artist's workspeed is proven to be fast and steady.
Either they make up their own shitty story, or they just insert filler CONSTANTLY like Bleach and kill their own anime.
If a manga artist is consistent with their pace, and they make chapters at a rate that an anime can progress at nicely then it's fine.
Too many anime jump the gun and rush into things when there isn't enough data to know if the anime will "catch up" to the manga or not.