[mrcaptainbob]

I'd snap a line down the center of the hall. This will all be dry fit first! One of two ways to go: The first is to lay a row of tiles side by side crossing the hall with their seams butting over the centerline. How much tile is left at each wall? hopefully most of a tile. If not, center a tile over the centerline and lay tiles next to it crossing the hall and then see how much tile you have left at each wall. Hopefully a lot. The idea is to trim as little waste from the wall tiles as possible. The further a seam is from the wall the less noticeable out-of-square is. Do the same for the length of the hall. Here you'll have an additional challenge of balancing out how much waste because of the two walls on the T part and where the final row of tile meet at the foyer. I would maximaize the tile at the foyer for appearance. As for the actual laying of the tile, of coarse you set down luan panels first. Gluing them in place is the best option. Make sure there are NO bumps or low spots that would telegraph through to the new tile. After that luan is layed in place, snap your lines again on this. Lay your first row lengthwise per your earlier decision. EVERY piece is layed with the thought of it being 'special'. Mind the directional arrows on the back to maintain correct pattern. When setting that tile, there will be NO moving once it makes contact. Trying to change it will only destroy it. As PERFECT alignment as possible is a must. It'll go remarkably quick and easy.
And above all.have FUN doing this together!!