This has always been an issue with the Dark Siders, as their downtime between the first and second campaigns mentioned- they can kill but they can't rule. They can kill pirate chiefs but don't have the support to rule pirate clans, and the same holds true for the Serpent- which is a galactic organisation anyway, and still vastly powerful.
In any case, you can't even hold the citadel! More enemies are going to keep coming.
So yes, one problem Dark Siders have is a lack of political power- or ability.
So we should have allied ourselves with one of the people in power here from the beginning, but nobody really supported my idea, even with Yago.
Ushgarak, the main problem is that it takes time and careful preparation to control criminal organization, not just killing the leaders, right?
And another problem: if we establish a power base then Jedi/Bureau would learn about it sooner or later, and destroy any organization we control, even if it would be overlooked otherwise.
What if we just run to Outer Edge/Unknown Regions and try to establish power base there? Could it be a good idea?
Oh, you weren't there to control the Serpent; it was an extended smash and grab. Trying to control th Serpent is like trying to control the Hutts- on that scale, it is not very practical for you.
Sidious goes straight for the throat with the Republic, of course, but he's the Sith boss and it took him decades.
The rest of your logic I totally and utterly agree with- it is exactly what you must do. The point of the new storyline is that the Bureau forces you out of the Republic.