The Jedi Order at present may be high on the fumes of stagnation and arrogance as a whole, made worse by Palp's and previous Sith Duos subtly blinding their ability to see through the Force and they may be mistaken about their traditions being the one correct way to go about being a Light Sider...but they aren't actually wrong that the Dark Side fucking sucks. I'd be very careful about making any attempts to try and have our cake and eat it.
As for which side to pick in the CW...that assumes we're going to be in a position to do anything about it. We don't actually have all that much time available to us, even if we rolled natural 20s every single turn. Imo we shouldn't declare for either side and should take the chance to either be mercenary and/or try our luck at taking on the Hutts. That said, even in our neutrality I do think we should have a slight Republic bias. At the end of the day, while Palps is playing both sides, the Republic does have some safety valves like a handful of 'sensible' and 'moderate' senators and the Jedi (who are ultimately good *people* even if they're blinded as an *organization*) whose better nature our Elder probably appreciates and can appeal to if our actions are framed in a sort of 'taking out the criminal trash' way. As for the CIS, it should be remembered that for all that there's *some* sensible grievances in there...their parliament/senate counterpart is a sham organization that Dooku and in turn Palpatine have far more direct control over than they do the Republic.
Assuming we can't do anything to stop O66, we should at least do our best to mitigate it which broadly just amounts to taking in Jedi refugees imo.
Ultimately I don't think this game is going to end in the timeframe or era of the Clone Wars. This is going to be a 'Long War', so to speak. Our ultimate enemy is going to be the nascent Empire (and Palps) and not anyone else, I'm certain of it.