1/3 hp...not possible (well, actually, anything is possible with a short circuit, said purely tongue-in-cheek).
Digital timers are tops. No real energy consumption until they kick over the switching to turn the plugged-in equipment on or off. Most use AA or AAA batteries (singly) for backup power, and they can run a long time on just that.
The new GE Grasslin timers use a NiMH integrated cell for backup power.
I think you are way off on your electricity costs. It's not as bad as you think it is!
If your timer truly is using 250W just to run itself w/ no load, you would know it intuitively...it would be uncomfortably hot to the touch, and would have deformed or melted plastic parts (i.e., it would be malfunctioning).
If it is really hot to the touch, you need to get unplug it and get rid of it...it's a fire hazard.
v/r, N-A