I did that years ago, and had no problem with the top. I had a flooring supplier drop a line of teak flooring that was sawed up into
12"x12" squares, and I got the sample pieces.
Here is what I did: I bought a piece of tempered masonite and direct glued the tiles to the masonite using a flooring mastic formulated for wood flooring. (Read here: elastomeric adhesive with great elasticity.) I used masonite because I wanted a surface that was completely smooth and had a hard, closed surface to retard the glue set time.
No nails were used on that part. I cut a pieced of plywood from the old scrap pile (probably B/C or soemthing like that) and then glued and clamped the whole masonite/teak floor top down to the plywood. Made a 2 1/2" rim to cover all the nasty edges from some complimentary wood stained to match the teak as closely as possible.
Screwed it to a used black iron pedestal table stand that I got from a restaurant supply.
It looks great. It works well an has not had any joint seperation or buckling because it stays inside the house where it is in a relatively stable environment. Before you put your planks down, leave them in the house for about two weeks to stabilize. Also, if you do use the birch underlay, then stabilize the surface with a good latex sealer (cheap, cheap) before glueing and/or nailing and those planks will stay on for a long time.
Robert