I wonder if the painting is based on the William Brown sinking in 1841.
1) The rescue vessels were probably British according to the museum write up;.
2) Birch was from Philadelphia, which was also the destination of the William Brown.
3) The William Brown sank in 1841 - the same date as in the painting.
4) And William Brown’s rather scandalous story probably stirred up lots of coverage, which increases the likelihood that Birch was aware of the wreck.
I love to speculate! 😼