I can't really help you in the sheet music department, but those bands are heavily tabbed out on the net. Also, Minor Threat and Black Flag (generally) have relatively simple bass lines, so they're easy to pick up by ear. Bad Brains is an exception, but I think with your jazz background you should be able to pick it up. It's unfortunate that no one's ever documented any of this stuff on written notation.
For the second part, pick playing for old school hardcore punk is mostly about 8th note downstrokes. This is mostly because a lot of those dudes just picked up a bass and started playing with no formal background, so it's all about unlearning a little of what you know, loosening up, and putting a lot of energy into it. However, I would just develop alternate picking (up-down) since it's much more efficient. Some people say you don't get the right tone, but with practice it doesn't matter. To develop pick technique, I would just run through some the exercises listed in the exercise sticky with a metronome. The one by Gyoon (#3) is specially made to develop pick control.
Excercise sticky
