I ran into the same thing. Here's what I came up with (which I'm fairly certain is actually RAW).
Typically, Thaumaturgy takes "a few minutes." That's 4 steps up the time chart from "instant" like evocation. So for any Thaumaturgy spell, you can do the ritual instantly (not counting additional rounds for gathering more power if needed) by increasing the complexity by 4. You can do the ritual in a single round (a few moments) by increasing it by 3 instead (but this means it will take at least two exchanges to cast, as you'd have to gather power on the second). Increasing it by 2 would mean you could do the ritual in two exchanges (taking at least three to cast, gathering power on the third, although this is an estimation it seems fair).
If someone helps you do the ritual, that's best represented by a Lore roll to declare "Assistance from Friend" on the caster. This would then be tagged for a +2, allowing you to meet the greater complexity easier.
So to break it down like you did, although these are just estimations of flavor:
Rushed Thaumaturgy:
Increase complexity by 2.
Round 1: Draw Circle, carefully.
Round 2: Set up ritual objects.
Rounds 3+: Gather power and cast.
Fast Thaumaturgy:
Increase complexity by 3.
Round 1: Draw circle and imagine ritual objects. Or grab ritual object and imagine circle.
Rounds 2+: Gather power and cast.
Mental Thaumaturgy:
Increase complexity by 4.
Round 1: Imagine ritual, gather power and cast.
The important thing with the flavor above is that the spell becomes more complex because you're mentally preparing more of it. The ritual is the construct to help you control the energy. Harry has said you can do this in your mind, it's just harder.
Now, in combat, it's likely you'll get help. Here's example flavor for that.
Aided Rushed Thaumaturgy:
Increase complexity by 3 (then tag "Assistance from X" for +2)
Round 1 (Friend): Friend draws circle OR aligns ritual objects.
Round 1 (Caster): Draws circle OR aligns ritual objects (whichever not done by ally).
Rounds 2+: Gather power and cast. (Friend may assist, adding taggable aspects to boost control roll).
Aided Thaumaturgy:
Increase complexity by 4 (then tag "Assistance from X" for +2)
Round 1 (Friend): Friend quickly sets up ritual.
Rounds 1+ (Caster): Caster mentally completes ritual, gathers power, and casts.
Quick Group Thaumaturgy:
Increase complexity by 4 (then tag "Assistance from X" and Assistance from other X" for +2 and +2)
Round 1 (First friend): Friend draws circle.
Round 1 (second friend): Friend two sets up ritual objects.
Found 1 (caster): Gathers power and casts.
Of course, to provide assistance, a friend must make a Lore maneuver, typically two shifts less than the complexity of the spell. I'd allow interesting things to happen if I were the GM and they failed.
Rolls complexity-3.
"Oh, that's okay. You didn't do much but it should work." Scribble down "Faulty Circle" or "Wrong Ritual" aspect.
Caster completes spell. Hand him a fate point.
"So your demon appears, but he just walks out of the circle." OR "Instead of the lord of dreams, you see a crow." OR "Your fireball shoots up into the sky...and you don't see it come down anywhere near by." "Your enemies all disappear." etc