How can one obtain a press pass to get around the filming permits?

You are either press or you're not.

Press goes out and documents, news, events...generally, things as they happen, for air. Normally, you would have to show some type of affiliation with a news agency or sell them on the fact that you are some kind of independent. Fib #1.

Shooting a film involves setup, rehearsal, blocking, staging and multiple takes, and more often than not, a larger crew. Going out and trying to do this successfully is really a roll of the dice. Fib #2.

If you do get a press pass and misrepresent yourself and you are challenged, chances are that, at best, you will lose the priviledge of carrying a press pass.

Worse case scenario... and this depends on the degree of assholiness of the authority challlenging you, can be several notches higher on the "what the hell was I thinking" scale.

Good luck, RB.