Preventing rot with the tiles is a great idea -- I guess it depends on how long you plan to keep the tree in there before repotting again.
I'm not an expert in building boxes and am hardly a carpenter, but this is how I devised a recent pot for a maple I acquired.
I used all redwood scraps from some boards I had lying around my garage from previously unfinished projects. I picked up some gutter guard metal mesh and stapled it to the bottom for drainage. I knew I'd be watering this maple quite a bit so I left a lot of drainage.
The bottom of the box has two redwood "feet" running orthogonal to the base to keep the box up off my bench so the water can drain freely. I used "outdoor treated" screws on the entire thing to prevent rust. I did not pre-drill the holes as this redwood was quite soft and I didn't fear any splitting.
The two high pieces were just placed there and not secured until I found out if they would be needed. Turns out they were not needed as I was able to clean the roots enough so they would fit in the lower profile.
Pretty simple construction and it seems to be holding up well. I will evaluate the box next spring to determine if it's holding up well enough to last another season.
Oh and redwood is incredibly light. That paired with my lava substrate I can lift this box no problem and move it around without issue.