The supervision line is the right thing to be bothered about, and it's the structural weakness of designated agency generally. Designated agency assigns a different agent to each side so neither individual sits on both, but the broker of record still owes duties to the brokerage's clients and still has access to both files. In a four-person shop with the listing agent as broker of record, the wall is a policy, not a physical fact. Some states address this explicitly in their license rules, including whether the supervising broker becomes a dual agent by operation of law, and that varies enough that you want your own attorney reading your state's provision rather than the firm's form.
Concretely, ask for four things in writing. Who the designated agent for each side is by name. What the broker of record's role is described as, and whether she recuses from your negotiation strategy entirely. Whether any information you've already given her, including your walk-away number and your reason for selling, has been or will be shared internally. And whether the firm's compensation changes at all if both sides come in house.
On your numbers, the 17k is the visible part. The part that costs you more is a soft negotiation. If the firm is holding a real 340k buyer, the alternative isn't losing the buyer, it's the buyer being represented by someone outside the firm, and the firm still gets 8.5k. So the firm's downside from you refusing consent is 8.5k, not the whole deal. That's your actual position when you ask for concessions.
What you haven't raised is timing. If this buyer's inspection turns up something and the price gets renegotiated, the internal-file problem gets worse, because the person arguing for the credit knows what your bottom line looked like six weeks ago.
