Honestly, we will need to talk with everyone to solve this issue. So why don't we discuss longer terms plans?
For example, I think we should talk with Padmé now, Palpatine later and finally with the Senate.
Talking with Padme now is winning, but she herself won't solve the problem. What will happen though, is start things in the Senate, because, as said before, it can tie Kalee and Naboo by showing how similar their situations are and this would be a way to threaten the power of the Senate.
After that, we talk with Palpatine, because the problem will only start to be solved with his help. Also, if I remember correctly, Palpatine is from Naboo too, so if we tie Kalee and Naboo this way, well, public opinion will easily turn against the IBC, and obviously Palpatine would use this masterfully in his favor, so the idea of helping us will be even more delicious to him.
Finally, we talk with the Senate, because now there's a movement on Padmé's side, and Palpatine will want to help us, so the usual bureaucracy of the Senate will probably be less of a problem. And if we are lucky to find some of the actually good people there, like Bail Organa, they will already know of us by that point and will want to talk with us too.
Of course, this is dependent on being able to choose to talk with Palpatine after talking with Padmé, but, well why wouldn't we?
EDIT: Also, we need to destress Anakin somehow. Too bad it seems every step we give towards that, we take two or three steps back.