Before doing anything too crazy, I'd double-check that the low point drain valves and the tank drain valve are all fully closed and don't have some bit of grit or something stuck in them.
I rather doubt that any slight bit of water remaining in the tank would cause it to crack or otherwise leak. There's plenty of room (horizontally and vertically) for expansion.
If you leave the pump on with the taps all closed, does it cycle periodically? If it does, that's a good indication that the leak is in the pressure part of the system. If it doesn't cycle, then the leak/drip must be before the pump.
