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Can someone please provide a link to where the Bahag gives his list of the 613 mitzvos? I've tried looking for it online but I haven't found it yet.
I read that he does not follow the Gemara's numbers of 248 positive and 365 negative commandments. Is this true, and does he have a different source for his number?
The introduction to the Halachot Gedolot with the list of mitzvot can be found here. It's worth noting that it is not clear whether this list was authored by the author of the Halachot Gedolot (the Behag).
He doesn't separate the mitzvot into positive and negative, but instead into (1) punishments (ie. mitzvot that get death/karet for not observing them), (2) negative mitzvot that get lashes, (3) positive mitzvot that don't get lashes, (4) parashiyot (ie. communal ordinances, that no one person is punishable for not observing them).
In terms of the number, the editor of the Hildesheimer edition of Halachot Gedolot wrote that it was not always clear how the author was counting mitzvot, and hence that the numbering given there is not unquestionable ("לעתים קשה לקבוע הפרש מדוייק בין המצוות... אין לראות את חלוקת המצוות המובאת להלן על ידינו כהחלטית"). Notably, this means the original author of the list didn't indicate separations between the mitzvot. The Hildesheimer edition counts 73, 282, 199, and 65 mitzvot in the respective four categories. That comes to 619.
In terms of the author's sources, it seems that the Talmudic aggada was not seen to be the only choice when it came to enumerating the mitzvot. If you look at early azharot (liturgical poems for Shavuot that list mitzvot), many follow the four-fold classification mentioned above, and don't aim to come to 613 (unless you awkwardly force it). See here for a more detailed question as to the source.
(Much of this information is sourced from the Hildesheimer edition of Halachot Gedolot and Daniel Goldschmidt/Yonah Frankel's Shavuot machzor.)
I followed the link, provided by @magicker72, and I see the Bahag clearly does say he is following the list of R' Simlai, and even reiterates that his list adds up to 248 positive commandments:
