Warmup
Weakened TCW Dooku should take everybody here one on one, Vader's lack of hand isn't as extreme of an injury as one would suspect given his inhuman durability and he would honestly have zero problems with anybody here. Bane, on the other hand, missing a lightsaber and even weakened holds no chance against anybody here, and would honestly lose to Ahsoka, while Ulic would lose in an extended bout against anybody besides Ahsoka. Yep, team clears this one, unless the opponents get extremely lucky and someone quickly takes out Bane.
It's not that Bane is so massively inferior to everybody else, he should be way superior to Force-less Ulic even when drugged with deteriorated Force connection, but being drugged, having to rely on damaged Force connection and melee abilities with no weapon... sorry, lol, he can only hope on prolonging any combat he enters.
Round 1
Damaged Dooku could potentially lose to TCW Obi-Wan, damaged Vader probably too, but they would beat everybody else. Bane would get slaughtered by TCW Kenobi in this state, Ulic would give everybody a fight, but would be still dealt with in short order. I honestly believe it is the most random fight here.
TCW Obi-Wan would deal with Ulic or Bane without much of a problem. Agen would engage in a prolonged fight with Dooku and lose only to Force abilities, similar with Vader, and he would take out Ulic as swiftly as Obi-Wan, and Bane wouldn't stagger him too much neither. Then you have Qui-Gon, who would lose to the better two, and win against the other two in a good fight, and finally Barriss who is a complete wildcard and would probably give some fight to anybody. It honestly depends on "who falls first".
Round 2
In their state, Dooku or Vader would have a hell lot of difficulty fighting with Cade, while the other two wouldn't stand much of a chance, similiar as with Obi-Wan. Talon, on the other hand, would probably destroy Bane real fast, since her power would disallow Bane from staggering her with the Force, and her powers should prove themselves an insane help against severed Ulic. Funilly enough, while she would deal with Bane or Ulic almost as well as Cade, she would probably stand completely no chance against Vader or Dooku. Wolf and Shado bring the team down though, and as DMB mentioned, they could probably win by exploiting this.
Round 3
This honestly stops being a contest. RotS Anakin slaughters Bane, whose diminished Force powers would be utterly useless to stagger him, overpowers Ulic in short order, or takes out Dooku in a great contest. Debatable against his older self because of obvious reasons. RotS Obi-Wan loses to Dooku or Vader in an inhumanly tough battle, and honestly, Vader would be hindered enough as a duelist that Obi-Wan could take him down before Vader would decide to retreat into Force power department. He would slaughter the other two too, although Bane would put up some resistance with the Force, but he can't take him out via sheer power alone. DD Vos would fare on the somewhat similar level, and Ventress would put up a good fight against the better two before inevitable failure. But still, team stands no chance. Opposition 10/10.