4 Legged capacitor?!

Yeah, I was wondering about a joule thief.

So, if I made the capacitor in my original circuit the power source for this:

which is straight from

do you think that might have more success?

Or would you have a particular higher efficiency constant-current switching regulator IC that you would recommend?
Maybe something like the 756 version of this:
http://www.digikey.com/product-detail/en/MAX756CPA%2B/MAX756CPA%2B-ND/1130177
??