Thank you for clarifying. As far as I can see, the first of those proposed solutions will result in a 'no consensus' result in the best case, as the account state will look to both lockers like each of them has the correct spend individually.
The second solution sounds like it will lead to all lockers being forced to sign all transactions as there is no way to tell there is going to be a double spend, so lockers from round A will have to be online to sign round B and so on and so forth.
I'm not sure why you'd think that would happen in the first solution, since the locker of the current round would only consider valid what the locker of the previous round says is the state at the end of the previous round. The locker from the previous round always trumps the one from the current round.
Both current round and previous round lockers signing on transactions would basically be an explicit version of this.
You wouldn't need to extend this to further past rounds, since honest nodes should only re-broadcast/accept transaction from the current round, or from the last x second of the last round. The duration of a round needs to be long enough so that a transaction can be broadcast to the majority of the network.
There's no way to create inconsistent transactions like this, the worst that could happen is that a locker signs a valid transaction that doesn't have time to be broadcast to the network.