Splitting by bookmarks halfway pages

Hi,

I have a number of songbooks / hymnals / fakebooks in pdf format. I've added a bookmark to each song (tried this bookmarking the entire page as well as the actual song title).

Tried splitting in Acrobat Pro on both Mac and W10, with the built-in split tool and the Autosplit plugin.

The problem is that some of the songs start on the same page as where the previous song ends. It kinda looks like this:

Page 1

-- Song 1 + BM1
Page 2
-- Song 1 (continued)
-- Song 2 + BM2 (tried bookmarking just Song 2's header as well, to no avail)

When I split this, "BM1.pdf" contains just the first page. I want it to contain the second page as well (either completely or until BM2).

Is there any way to accomplish this? Or can I just force Acrobat to split by 'bookmarks + next page'?