Richie,
I've found a copy of Dixon's 'Traditional Versions of Ancient Ballads'
online, but it does not contain BBA. However, the lengthy and very different versions of the 17 ballads from the BL ms have Peter's signature all over them. No wonder Child chose not to include them.

What would be really interesting is if any of Peter's verses are the earliest appearance of those verses later found in oral tradition. If Dixon didn't print it then it's hard to see how these verses could have got into oral tradition unless they already were part of oral tradition or Peter printed them on a broadside.

I must hastily add there are some great versions of folk songs in there and some of them do look genuine. The earliest extant version of The Herring's Head is in there.