Welcome to the site. I'm PDtax, and will be helping you today.
I was going to suggest using your own foundation, and a few other ideas, but I need to grind a few numbers first. Zeroing out the tax debt will be hard with AMT. You may need a combination of things to get to zero.
I'll get back to you later today.
Let's assume the capital gain has not been taken. The Federal capital gains tax rate and AMT apply. Let's assume 2013, and its 20% tax rate. If taken, $340,000,000 would be due (approximately).
Donating some of the appreciated stock would be limited to 30% of income (special rule). Establishing a charitable donation in which you gift appreciation as the donation (which increases the value) can get you to 50% of income. Giving some of your stock to your foundation pre-sale would allow that gain to escape taxation, but you still have the remaining 50% and AMT to consider.
A combination of AMT-allowed tax credits could be used to drive the tax debt down farther, but that system exists to eliminate just the scenario you propose. It may not be possible to get to zero any more without owning active NOL generators.
Thanks for asking at Just Answer. I'm PDtax.
For some reason I expect some arcane rule to apply wherein if (say) an individual gives 90% of their income away, they would have no tax burden on the remaining 10%.