Thanks for the compliment!
And sure, you could bring in BDP skills and even change the rules on how they apply, whatever works for your table. The rules are pretty modular so flavor for taste.
On Push, Bleed, Brutal, it came down to not many weapons being covered by some abilities compared to others, so for the sake of simplicity I narrowed down the list. But you can certainly bring them back in.
Enjoy and please let me know how it goes!