Replacing exterior door threshold with 2" between door sweep and concrete.

[JJR2]

Installed a new exterior door, fiberglass with rubber sweep at bottom. Need to install new threshold on concrete. Original door was slightly longer, and aluminum threshold was installed by laying a strip of tile to extend floor under inside edge, canting the threshold at an angle. New door is shorter, so that with tile strip removed, total clearance to door bottom is about 2". Replacement aluminum/rubber thresholds I can find come about 1 1/8" to 1 3/8" thick. How can I make a sound installation that fixes this problem?