I haven't used a SWP yet, but I've read up on them plenty. It seems to me that unless your galvanized mesh screen is very fine, you will have trouble keeping the growing medium and the water reservoir separate and you'll eventually have much less room in the reservoir for water as that space collects medium and, perhaps, roots. Too, as the tree becomes rootbound, separating the reservoir from the unpotted tree could prove very difficult - better cut off any lip on the reservoir bucket. It's an interesting idea, though.
How do you plan to wick the water from the reservoir to the growing medium?