In solution #2, when an encrypted message is received, does the receiver have to lookup the sender's specific key from a list that they maintain? In other words, does every member have a list of every other member's special group keys?
This is more or less equivalent to having a single shared group key, but there are some practical reasons why it's split out. I think one of them is that it makes symmetric key ratcheting (for the purposes of perfect forward secrecy) a little less disastrous in the case of out-of-order or failed message delivery. Not totally sure, though.