Why is it so complicated?
Normal circumstances: I draw power, cast a spell and take mental stress
Circumstance where magic is locked down: You can't cast spells. So, in advance You may draw on shifts a number of times = to your conviction. You use those shifts to cast spells normally until the shifts are gone. Why would you be able to avoid mental stress? Each spell works like evocation normally does. You take mental stress. You can cast spells until you have no stress boxes/consequences left or you have no shifts left - whatever comes first.
Note: you cannot draw more magic until you've completely depleted the pool you've gained. This prevents people from going: "I draw 44 shifts. Next scene: I draw 44 shifts. I do that 20 times until I have oodles of shifts making the lock-down an un-challenge"
If you do it this way, there is no in-game benefit.
I see this as a very specific challenge. You'd never use it except in that very specific circumstance. With 44 shifts, you could preserve your energy by casting less powerful spells, but you'd go through your mental track quicker or you could cast less, more powerful spells and end up running out of your pool. The latter doesn't happen in a normal combat.
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The other way is setting up a bunch of aspects, as dmw said, and invoke them.
GM: you can't cast spells here
Player: I created 3 aspects in advance that let me cast magic, I'll ivoke.
When you run out of tags, you start spending FP's so you can cast.
and/OR
The GM says: there's a "magic dead" aspect on the scene I compel you not to cast." You earn a FP. The next time you want to cast, you spend a fp to turn down the compel and cast your spell.