Well Chuck has just over 1000 full-round actions, and you're above him by a factor of 4 (good job!), so you still need 250 times more. That's 8 Doublings.
You've secured the attack number for a single action, so you've earned a place in the record thread. Now to make the number as high as possible...
He's at 200 million? Thought he was at 2 million.
And 4 base doublings would cover it, since each base doubling is a x4 to the off-hands.
Some time ago I cranked up the "CO's Response to Fastest Possible Speed" version into THIS monster:
http://forums.gleemax.com/showthread.php?t=993832THAT Chuck broke the speed of light, which doesn't sound like much in Theoretical Op, but when working off purely finite game mechanics it's not an easy thing to do.
1,104 Turn Undead attempts. Each translates to a Swift Action which translates into a Full-Round Action with Greater Celerity Shenanigans.
Base Speed is 1152140 ft, and he can travel twice that in a full-round action and every 10 ft is a throw.
So 1104 * 230428 is how much Chuck can make if he only cares about attacks and not damage. For damage he starts out with some Run actions to improve the average.
So that comes to...254,392,512...
4 doublings(assuming the doubling translates to x4) would give you 241,905,664. Add in a couple attacks of anything and you've got it.
Even if you fall short, you've already impressed me by how many you're making with finite game mechanics. If nothing else you can be called the "Million-hit Monster"