Absolutely correct. This is pocket lint to Bank of America. The big banks operate at an absolutely mammoth scale; BoA has 208k employees. More consequential mistakes than this happen by the thousands every day. There is, quite literally, a budget for it.
It is an unfortunate reality for the US that you have to present as a savvy professional, but as soon as BoA is institutionally aware that there is a savvy professional who is at the point of involving a lawyer, I give them ~48 hours to make the decision internally "We're totally paying that" and a total resolution time of under two weeks.
If it were me here, I'd ask for the branch manager at my first visit immediately after getting the run-around from tier 1 CS. I give better-than-even odds that the branch manager can self-resolve this, particularly for a longer-term customer or relationship they'd otherwise have reason to care about. If the branch manager isn't super receptive to that immediately, walk into any lawyer's office and say "I want a letter written to Bank of America saying that they owe me $X plus whatever you charge for the letter." (If you for whatever reason can't afford a lawyer or can't get a lawyer to take you seriously, you can get much of the same effect by saying "Regulation E" on paper. [+])
Your lawyer won't even have to threaten a suit over this. Everyone knows the score here.
(I use to ghostwrite letters to banks. One of my weird hobbies.)
[+] Regulation E governs electronic funds transfers at US financial institutions. People who know that are very dangerous people for banks to annoy, because Regulation E contains a state machine which is very consumer-favorable, and there is an implicit threat of "I bring your operation of the state machine to the attention of a bored regulator who has no joy in their life other than opportunities to hold your feet to the fire for improperly operating state machines."