First of all: thanks all of you for the very thorough responses!
How much are you micromanaging the squad? I like to dock them behind the procurement and upgrade terminals. Then they should be relatively safe to spam powers. What builds do you have on EDI and Garrus? Does Garrus have Proximity Mine with the Damage Taken debuff (it helps).
The Vanguard is sort of tricky since he can charge and Nova. There is a small window where you can dodge after he charges you. Squad mate powers can also cause some stagger if you hit him at the right time.
Your weapon choice isn't the greatest, but it should still be doable. Suppressor is the best weapon for this fight (with Cranial Trauma if you have it). Of the two, stick with GPS. Hold to charge it, then you can use Biotic Charge against the clone. In the mean time you would be using squad powers to setup combos. So EDI Overloads, you Charge, Garrus Overloads, you Nova. Depending on how comfortable you are with Charge-Nova and Nova-canceling you could potentially do the whole thing powers only, but might as well fire the GPS as well.
Well, I guess I'm not micromanaging the squad that much, I just keep close tabs on their ability cooldowns and try to use their powers as much as possible, timed with my own attacks. I can't recall what builds the others have, other than that Garrus has the Armor Piercing Ammo power shared with the rest of the squad, but I can check. I think EDI has the Arc pistol and the Locust, while Garrus has the Viper and Geth Pulse Rifle, but I'm not one hundred percent about that.
I've tried charging the shotgun for better effect, but since that means leaving cover for awhile it's always left me an open target for enemy fire. I've had my powers on cooldown at that point most of the time (I take out the shields with Energy drain before firing), resulting in a mission failed pretty soon after. But I don't think I've tried the biotic charge immediately after and that should refill my shields, so if I save my powers until after the shot and do as you say it could work! I'll definitely give it a try, that and try to position my squadmates better, and if it doesn't work I'll probably reload and follow your advice on other squadmates/weapons. 
Just a slight emendation: I would overload with Garrus first and only Overload again with EDI if the Clone still has shields. Otherwise, if the Garrus-Overload/Charge tech burst manages to strip the shields, then use EDI's incinerate since that will work better against armor.
I will say, the easiest fight I had was with James and Ash. Grenades are a beautiful thing, especially Ash's inferno grenades. They can use grenades even if they are on cool down. So if you find you want to use a power and can't because they are on cool down, you can just choose to use a grenade instead. (Another factor in the ease of the fight was probably that I had given both of them Typhoons.)
You make valid points, the fact that EDI has both overload and incinerate is the very reason I brought her along. What you're describing is exactly what I've been trying to do, but I must admit I'm becoming more and more tempted to reload and swap EDI for a more tank-like character with grenades, preferably Wrex or Vega, because one of my big problems has been having all our powers on cooldown. I didn't even think about the possibilty of using grenades when I chose my squadmembers, I somehow seem to forget about those all the time. Probably because I'd like to imagine that I am tank-like enough for the entire squad and therefore never bring any of the buff characters with grenades on a mission - haha, I guess that's hubris for you... ^^;
I was playing on hardcore but just in case you haven't tried this:
Literally all I did was ram into my clone non stop with charge, followed by a shot with my Disciple shotgun (the Disciple's stunning ability probably helped) Rinse and repeat. Nothing else. My squadmates do fine occupying everyone else (I had Garrus and Wrex)
This way I had my clone in my grasp every second, cause not being able to keep track of her is when it becomes a ****storm since she moves so fast. Eventually I drained her health enough to get to the cutscenes, and being able to charge after every shot with my Disciple basically made me untouchable by Brooks/mercs.
I am suddenly wishing I had upgraded my disciple shotgun, the stun function sounds very handy - I hadn't picked up on the fact that it had one. :/ And yes, the fact that the clone is superfast seems to be the main problem. She doesn't even seem to have to wait for her powers get out of cooldown? So unfair! No matter what I do she insta-stalks me all over the room, it's very frustrating. But I'm going to try the whole "charge a shot and then biotic charge the crap out of her"-approach and see where that gets me. 
Thanks again, all of you, for the input! Now, I've got a clone to get rid off - she tried to space my space hamster, so she need to be taught a lesson... I'll let you know how it plays out!
UPDATE:
Haha, okay it was kind of a cakewalk this time around. Got to the first cutscene real quick, then it took a few more tries to get to the final cutscene, but it was WAY easier when saving the biotic charge 'til after firing a shot. I think I ended up chasing my clone out of range for Garrus though, all of a sudden his Proximity Mine power was locked. Didn't matter in the end though: ding dong, the witch is dead! ^^ Thank you so much for the help! 