To say the very obvious just because I want to write down my thinking: This feels like a vote where we need to balance the effects on Anakin vs the effects on the galaxy, more than just how effective the vote is at the task.
Naboo being the best long term contact, but the least effective at getting the task done.
Shiv being the most effective way getting the task done but the most dangerous to our sanity.
I think the senate is honestly useless. I can't imagine them NOT taking the opportunity to set a precedent of power over the Jedi, and the only benefit being meeting the future rebellion when it falls, as others have said.
I admit, I kind of wish we could take the option of "that's nice you think you have the authority to stop us, feel free to send the paperwork for legal consequences to our lawyers where they will laugh at you" but chances are they will try to use force to block the relief efforts.
But even that should work to our favour with any decent PR efforts. It's a lot easier to hush something that's never happened than block "Bank uses armed Armada to prevent Jedi humanitarian efforts" across the media