Hello friend. I have a 37 sorcerer (closing in on 38) and I'm also finishing Taris. I did the first few quests on Quesh and they were significantly tougher, since everything was basically my level. So back to Taris for me, I'll finish up and get 38 before moving on.
I've gotten pretty good at anticipating the moments where a cutscene will trigger. One thing I always do is bubble my companion, then myself and I RUN forward and trigger the cutscene. There's no timer on buffs during cutscenes, so when the fight starts we are both still bubbled. If there's an elite, I let the companion start the fight (as I'm sure you do).
I'm Lightning/Madness hybrid, so I have the 2nd-tier Lightning talent that buffs the shield barrier by 20%. Makes a huge difference. I also have Wrath in the Madness tree, so once my companion has aggro, I drop both Crushing Darkness and Affliction on the target, then check Khem's bubble. If it's too early to refresh it I'll start Force Lightning, and if Wrath procs then I use Crushing Darkness (if it's up) or Lightning Strike. Re-bubble Khem, reapply DoT's, heal Khem if needed, then Force Lightning until dead. I'm confident dealing with a solo elite this way, they rarely ever defeat us. Khem never seems to lose aggro, the only time he does is when he gets controlled (such as Force Lift or Force Choke) at which time the mobs head straight for me. At times like that I use Electrocute, Force Slow, anything I can to slow them for a few seconds until Khem regains aggro.
I actually used Andronikus for the entirety of Alderaan, but we were always 2-3 levels higher than the content. I turned off his grenade (so he wouldn't break my CC) and I'd Whirlwind elites or silvers until all other mobs were dead, then we'd focus on the stronger mobs. It worked great, but after all that I am finding that Khem is the safer way to go. I've tried Ashzara a few times and just can't get her to work, for my playstyle. For groups of normal mobs, Andro and I blow them to bits. For anything tougher, it's back to my buddy Khem. Good luck to you.