My experience has been that BoA reports the statement balance. Mostly.
My due date is the 16th. Statement date is the 19th.
I always pay by the due date (except once, see my footer). On some occasions, I've made an additional payment on the 17th or 18th (sometimes by cash in-branch, sometimes pushed from my checking account with a different institution), reducing the statement balance; BoA has reported that lower statement balance to the bureaus.
That said, in July or August of 2017 (when I was in the middle of a mortgage refi, of course), BoA reported a higher balance than what was owed on the due date / statement date. I'll repeat: it did not report the statement balance, but reported a higher interim balance. I was displeased, and let the bank know it. The gist of my conversation with the BoA rep was that the bank had, well, engaged in anomalous behavior; it should have reported the statement balance.
@HeavenOhio wrote:I'd bet that paying cash will cause your payment to post very quickly.
Because there are so many BOA cardholders here, we'd have heard by now if they did anything other than report the statement balance on or just after the statement date. I'm sure that one of them will chime in to confirm.
Of the large, well-known banks, US Bank and Chase are the exceptions. US Bank reports on the first of the month. Chase report the statement balance on the statement date, but they also report zero whenever one pays to zero.
That's I love chase payments 
This is my first time with BOA. I wouldn't have this problem if they were closed last 2 days lol
This is my first time with BOA. I wouldn't have this problem if they were closed last 2 days lol