Thank you, raikado-san.
"All his friends like him" seemed redundant to me, so I thought I'd missed something in understanding the construction. After all, friends are supposed to like each other.
Now, if 皆 were to be taken as an adverb, (I just noticed on Jisho that it can mean "completely"), then it could mean "His friends really like Taro". That makes more sense to me. Particularly as you explained that this final clause should be understood as having an implicit それで at its start, which would mean it is the logical consequence of the first two clauses, (Taro is enthusiastic, Taro is considerate, and so his friends really like him...).
So to sum up, I had a feeling that I was having a problem with 皆 and wasn't sure where it should belong, modifying 友達, or as an adverb modifying 好きです. I don't have enough knowledge of sentence structure to be confident.