As for speed your characters are definately fast enough to solo all of phase 4 as well. While more speed could help, then that is not what prevents you from soloing phase 4 (super speed might help you take a bigger chunk of phase 2, however). A few things to consider:
In phase 4 the tank only takes 1 turn every time it comes out of topple. In phase 2 it takes 2. on top of that in phase 4 killing the two droids boosts Assaj' damage even more. Hence the damage potential is much higher in phase 4 than in phase 2.
To delay enrage make sure that the tank doesn't take an extra turn between tooples. Until Assaj' damage gets boosted enough, make sure to kill the adds/small guns ASAP.
Furthermore, make sure to have all special attacks ready when you enter phase 4 from phase 3 — especially illuminated destiny. This will help you kill all adds / small guns before the tank even takes the first turn.
Furthermore, find a good rotation between using Thrawn's, CLS' and Assaj' specials and using their basics. Using specials both refreshes their secret intel buff (preventing them from dieing to air strike and top canon) and it also reduces the CD of illuminated destiny, making it available more often for the big damage boost. It may seem counter—intuitive, but I myself always use Assaj' AoE once every topple in phase 4 for this reason even if there is only one enemy. After I begun to do this, secret intel never fell off her again for an unfortunate death by airstrike. My rotation with CLS is : Second special (TM gsin and self healing) — basic — first special — basic — second special etc. Hence I always use his basic right after his second special even if the first special is available. This is simply to make sure to use his specials as much as possible and not choose 'the wrong one' if both are a ailable.
Others already pointed out that having Ackbar die early actually helps you in phase 3, since CLS will always be called to assist (with his TM reduction on basic). I always remove his mods before this battle to ensure a quick death.