Going through the mountains in economy mode, an ebike wouldn't be much faster (if at all) than a regular road bike, as it would be slower on descents and because the economy mode wouldn't give you much power to go faster up hills, especially considering the extra 25-30 lbs of weight you're carrying.
Ebikes really shine when using higher PAS modes up hills and on flats, but don't offer much assistance in economy mode.
If you're doing a century, I think you'd want four 10Ah batteries and a medium-to-high assist mode, with three of the batteries being carried by a support vehicle! ;-)
I've got an 8.7Ah battery on a 48V/500w system and I get ~19 miles of range in the highest pedal assist mode, so you could probably get 25 miles per battery if you go down one assist level if you're running a similar setup, but then again, the mountains might sap your battery's energy faster than in normal around-town use.