Ideally one would sign a transaction and pass it to another person, and the transaction is passed down until it gets enough signatures. The next person might not be available or reliable for signing, so by chance you’ll need to try somebody else.
So you may as well just broadcast the signed transaction e.g. on the forum and just let the first FLOT member who sees it do the job. After this next person signs the transaction, he will need to broadcast the transaction again, and the signer that goes after him will need to sign this newly signed transaction.
Two people might try to sign the same transaction at the same time, producing a fork. Practically there’s only one valid fork but it means one of the two people would need to sign again, this time the transaction signed by the other one of the two people. There are coordination issues but it isn’t serious, we just need a protocol that has locks and timeouts on top of the broadcasting.
By the way, once the group is formed we’d be creating a first multisig to receive the current balance of Tier 4 and that likely requires coordination within a forum post. We’ll see how smoothly that goes.