Battery charging using low power density piezoelectric device
2.5 V isn't really all that small.  A Schottky diode will drop less than 1/2 a volt, so while the drop will be significant, there is still plenty left over to do something with.

Keep in mind that a 2.5 V sine has peaks of &plusmn; 3.5 V.  Even if there are two Schottky diodes ultimately in series in the path, that still leaves over 2.5 V just from a dumb passive full wave bridge.  That's plenty to run a low power switcher from to dump a little current occasionally into a battery.

Once you have a little voltage built up, you could possible use active synchronous rectification to increase efficiency.  Or, you could use a charge pump configuration with two Schottky diodes to get over 5 V out.  You could charge up a decent size capacitor until it gets to 5 V, then discharge it thru a switcher to charge the battery until the cap goes down to 2.5 V, for example, then repeat the cycle.

You actually have quite a bit of voltage to work with.  The trick will be to have very little quiescient current when nothing is happening, since you don't have a lot of that.