718,000 OR 702,300
EDIT: I'm leaving on my trip soon, so I don't have time to wait. Here is an extra score from a run that does NOT use the charged punch against the third boss. Bimmy, please use this lower score if you rule against this technique.
Time to go on vacation, so this will be it for me.
I'll pass along a hint that I learned last fall (where have you gone, Miss Clawful?): For extra points against the third boss (the green, splitting ninja), use charged punches. They will immediately trigger his split move, rather than requiring the usual three hits. This will produce more ninjas than you would normally have to fight. Each of these enemies is worth 1,000 points, so it adds up!
Also, make sure you kill all of the fire ninjas. Those are also worth 1,000 each, but they won't spawn unless you scroll the screen at the right moments.
P.S. - Loved the "burger" video. Couldn't stop laughing at all the craziness.