The user isn't going to have any legal way to transfer the data between backends anyway, since no transaction can see results of an uncommitted other transaction. There *has* to be some backdoor channel involved there, and you might as well make it carry the data without the user touching it.
The whole thing seems a bit backwards anyway. What you'd really want for ease of use is some kind of "fork this session" operation, that is push the info to a new process not pull it.
Is it a good idea to fork this new process under the same transaction id?. In that way the backends will be seeing the same versions of data among themselves.... Are you mentioning the same here?