Well, let's see here. 26 shift thaumaturgy spell with the speed and methods of evocation... Alrighty.
Let's assume the character is submerged, and built expressly for casting this one spell. So, discipline 5, conviction 5, lore 4, endurance 3, let's say seelie magic, and an extra two refinements for more focus item slots. Let's further assume that you can use two separate focus items in a single spell - one for power, one for control - this is of questionable legality, but let's run with it anyway. So you're dual-wielding staves - one with +4 control for (say) offensive summer magic, and one with +4 power for same.
(There are some other builds that might work better, but this is the best one I found that follows one of the existing templates - changeling, to be precise - and is also free of Lawbreaker powers.)
Casting the spell, step one: call up power. Since you're using the methods of evocation, you have to call up 26 shifts of power all at once. Well, conviction 5, +4 from the focus, so one mental stress would buy you 9 shifts. Four mental stress (checking off your highest stress box) is another three shifts; you're up to 12. Need another 14. Well, your minor, moderate, and severe consequence slots total up to 12, and you've got an extra minor mental consequence from conviction 5 - so there's your power.
Casting the spell, step two: control that power. All of your consequences (except extreme) are checked off already (just from calling up power), so you can't afford backlash that goes above your stress track. Assuming you're insanely lucky and roll a +4, you're looking at a base control of 13 (5 from discipline, 4 from our control staff, 4 from the roll). You need to come up with another 13 from somewhere. Well, let's start with backlash - you can take up to a four stress physical hit (thanks to your endurance of 3). Down to 9 shifts left to control. One point of sponsor debt and four fate points (not an unreasonable assumption given your refresh of 4), and there you go. In fact, that's one point over, so you could get away with a mere three shifts of backlash.
And if you got unlucky and rolled a -4 control instead of +4, well, there's always that extreme consequence slot to soak up more backlash...
(Of course, a truly canny player would have supplemented the above with a few aspects via maneuvers or declarations, and would have a bit more wiggle room for not rolling perfectly. But still, I think you get the point.)
So, conclusion: totally possible to cast a 26 shift thaumaturgy spell with the methods of evocation. Of course, you'd better hope that's the end of the scene, since you've just burned all your consequence slots, fate points, and two high stress boxes; a random thug with a rusty spoon could take you out at this point... (On the other hand, if you're an actual Wizard, as the original post proposed, you've got things rather worse - you may have a specialization bonus from evocation, but you're going to be missing the overpowered dual foci, and you'll have rather fewer spare fate points; still doable with some prep work, or maybe as a death curse...)
I'd also note that the character build used in this example, while at least mostly RAW legal, is not something I'd be likely to allow to exist in any game I was running.