...She defers to your expertise in this matter.

Speaking of expertise: Sheev, you're not the only one who can seed conspiracy theories.  Have fun trying to get buy-in when she and hers got there first with some carefully calibrated 'leaks'.  (They're not actual leaks.  They just happen to be just true enough anyway.)

They're very good succession laws! The best! Tremendous!

Formerly the Senate could appoint a new Chancellor by a two-thirds majority after their death, resignation or a vote of no confidence. 

However, many people were rightly upset about that! Chancellor Valorum was popular! There were many concerns about civil liberties and the security of the appointment process, and Chancellor Palpatine was extremely passionate about candour and transparency and the integrity of the political system, and even in wartime put tireless effort into making absolutely certain no such thing could happen again without proper mature oversight and august deliberation.

Of course, there had also recently been a rather frightening assassination attempt on Senator Amidala! She really doesn't have much luck, does she. So it was also paramount to secure the Senate against tactical assassination. 

Safety first!

At last count, there are seventeen different Senate Committees charged with various forms of, ahem, election fortification, endowed with a dizzying array of legal and military powers. Chancellor Palpatine was also passionate about the separation of powers, and has arranged for the Senate to form a series of factions with various complex, overlapping and unclear responsibilities with extremely important titles, while the Chancellor personally oversaw only a few unimpressive core functions, such as military and intelligence and internal security and the judiciary, since after all there was a war on.

Naturally, the Senate cannot bind its future self entirely. But a unanimous vote to change any of this is only reasonable, in wartime. The Senate is terribly, terribly important, after all. 

...Plan 'Oh Force why do I have to make this argument' is going to have to be a go, then, unless anyone has better ideas.  Because someone needs to unfuck this mess and clearly the Senate physically cannot do so.

Could they possibly simply take over to ease the transition?

There is precedent for Jedi to serve as Chancellors in times of significant turmoil.

It is, however, possibly exactly the sort of thing Sheev is going to try to wage PR on them with - like how he tried to frame them for murder - and disrespectful to the letter of the rule of law, though perhaps more respectful to its spirit than one would think.

Either way, they really shouldn't dump the Chancellery on Senator Amidala - or someone else, if the Jedi take over for just long enough to appoint someone else to undo everything, Bail Organa seems to actually be decent - without actually asking them.

"The danger from the droid armies - gone, it is not. Dooku's heart, difficult to see, always it was. Brief is this window in time, before the Senate can meet, before the Republic can crumble. Speak with him, we should, yes. But matter it will not, if no Republic there is left to bargain with him."

"We can do it. Take the Senate building, explain to the Senators what happened. Dissolve what Palpatine did, roll back to before the war. Then hand over to - Senator Amidala is a good choice, if she recovers, but we'd need to handle the Skywalker problem somehow. And I have no idea how the secret marriage issue is going to play out. I'm not a politician. Mercifully."

"Masters... is it worth risking the Jedi Order itself? If we get this wrong... these thoughts are leading us to a dark place. We are not meant to rule."

"...If there's any time for that to go public, it is, I think, now, when the galaxy is already in turmoil.  We fold Anakin's heroic reputation into Senator Amidala's - assuming it is her we put forward - and - I don't think you'll see it the same way I would, but the public will eat up this story of a secret love during these terrible times, as a thing to soften the impact of the rest of what's happening."

It is humiliating in a twisting way to be sitting here, having lost the Republic as he believed it to be, lost the Clone Wars, narrowly escaped the death of the Jedi, and be sitting here taking political suggestions from a Sith Lord, like publicly admitting that one of their most celebrated Generals flagrantly violated the strictures of their Order and pretending it's romantic. 

However, such feelings are beneath a Jedi, and in a moment he is himself once again. One way or another the Jedi must interface more with sordid politics, and being angry about it won't help. He will have to learn politics, very very quickly. 

"It's an irresponsible gamble. But so is literally anything we could do in these times. The shatterpoint in the Force has led us well so far. The question then becomes what to do about Skywalker. That boy is dangerous."

It is romantic.  It's just also something that Skywalker is probably going to have to leave the Order about, just, softly so - which, honestly, she thinks everyone may well be happier for anyway.

"...Train him better, obviously.  I don't think he knows everything you expected him to have learned, as skilled as he is in other areas.  And he needs therapy, because he's been being groomed by a Sith Lord since he was a single digit number of years old.

"He may be dangerous, but focusing on how he is a danger in how you handle him is just going to make the problem worse.  He needs support, not tacit vilification.  He came to your Order with scars enough already, as I understand it, and I can't imagine you handled that any better than you've handled him since then."

They gave him literally Obi-Wan Kenobi for a Master, come on. 

"We are the only people in the galaxy qualified to handle the corruption of the dark side. Clearly it wasn't enough. We can't just allow a Dark Jedi to wander around and hope he gets better. We'll need some way to secure him."

"...I don't think it would be good for Anakin to make him - retire. Believing that he's doing good is important to him."

If Obi-Wan Kenobi actually already knew how to handle raising a child inherently traumatized by slavery, save by apparently having been one himself and hopefully having received appropriate care for his wellbeing in the aftermath, she'll eat her mask.

"...You'd know him better, then.  It's still worth asking.  There's plenty of good he can do beyond the Order's ambit, and he's already done so very much.  Some time off might be very good for him, though it's not my place to say why I think he should take that time now."

"...Master Windu...  Dark is not a thing that you are, it is a thing that you do.  Notwithstanding that Force signatures do reflect one's habituality in that way, putting someone in jail for a crime they haven't yet committed is very kriffing stupid.  And I reiterate that as far as I have seen, he is not truly Fallen yet!  He has been holding the Darkness back through sheer force of will because he did not want to Fall."

"It's a thing he did. He clearly did not want to not fall as much as he wanted to lash out, in that moment. That is not good enough. That is not safe, in a Jedi of Skywalker's power. I'm not saying we imprison him. I'm saying we keep him under guard in the Temple."

"Yes, that will certainly calm him down."

"This was your failure too, Obi-Wan."

"He has done no harm as yet. Being - carried away - in training does happen."

"And if we let him go, what happens the next time he gets carried away? When you aren't there to protect his next target? Have you ever snapped a man's neck with the Force, Obi-Wan? It is not so difficult, not for a Jedi of Skywalker's power. We are charged with the safety of the public, not Skywalker's happiness."

"Mm."

He has not said very much. 

"So would we have thought. All my life, since to the Council I rose, so would we have thought. Well did it serve us some centuries. But if to our ways we had held, lost, we would have. With the safety of the public, mm, are we charged, not with keeping to procedure, hmm?"

"Yoda, you can't seriously be suggesting-"

"No. In all humour am I suggesting that we find another way, with Skywalker."

"I will reiterate, Master Windu, that I actively provoked that response.  I shoved his face in every trauma that traumatized boy has ever had.  Of course he lashed out.  Fight, flight, freeze, fawn, and he has been trained to fight, hasn't he?

"And I do not suggest that nothing should be done.  Just that, based on the evidence I have..."

Actually.  The Order doesn't seem to have evidence of anything he might have done, but what evidence do her sources have?