Clamping Schottky Leakage Current
Yes, the leakage current of D1 causes a voltage accross R1, which lowers the on-state voltage.  Use a lower R1 or a better diode.

There are other Schottky diodes that have less leakage than 2 mA.  Even this one probably has much lower leakage at 25&deg;C.  If you know it will always be operating at that temperature or less, then you can use the lower leakage figure.  If it has to work at high temperatures, then select a better Schottky or perhaps resort to a ordinary silicon diode, like 1N4148 or equivalent.  That's a nice and fast diode, but will have higher forward drop so therefore clip the undershoots at a lower level.  Everything is a tradeoff.