On the core question, no there is no way to bypass your agent and get ba to do changes directly with ba. Your agent “owns” the ticket and ba won’t touch it so you unfortunately have to keep discussing with your ta till you find an agreeable solution.

many TAs are very, very bad or disinterested when it comes to these situations just trying to select whatever the airline proposed but they have a trade number to speak to ba if they can be bothered.