This is a fine place to discuss it, as this is a project that Alba is contemplating. If rou feel this might be more of a covenant project, then Covenant Discussions (OOC) would also be suitable.
Aside from the exact dimensions (see later), the calculation of the magnitudes seems fine. Note that with 1 magnitude for complexity (the other one being for flexibility) you should end up with a fairly plain construction -- no carving or decoration of any kind -- because all the complexity goes into the layout. That's where the 3rd complexity magnitude of Conjuring the Mystic Tower goes to.
As for the dimensions, the basic Individual ia 1 cubic pace, 0.75 cubic meter or 9 cubic feet (the unit of measurement which is more useful for a lab design). So adding +3 Size would give you up to 9000 cubic feet.
Now, since you want a domed ceiling for the hawthorn, as well as a gallery above it (I can't find the drawing you posted), I'm guessing you need at least 20 feet in height. That would only leave you with a 450 square feet for your lab, which on the small side. Looks like you may need another magnitude for Size...