How can I maximize the tax deduction for donating shares that are not publicly traded?

Next year, I will earn a large number of shares in a company that is not publicly traded. They will be taxed as ordinary income at their 409A value, say $10. The company will be buying back stock at $20, but only up to a very low limit, 5%. In other words, I'll have a large windfall in income on paper (i.e. my tax return), but very little cash to show for it.

I want to plan a large gift from this windfall, and I want to maximize the deduction for my taxes. I've heard of donor-advised funds (DAF) and other vehicles for donating shares. If I donate shares instead of cash, what value can I deduct on my taxes? The 409A value ($10)? The buyback value ($20)? Some other value? My opinion is that the fair market value is $20, and that's what I want to get for my deduction.

If I can only deduct $10, but next year the company does another buyback at $20, then the value of my gift once it is converted to cash will be the same, but the value of my deduction would be much less than my gift. If I hold the shares until next year's buyback and then donate cash, I'll get a $20 deduction, but not in the same year as my windfall income, and I'll owe capital gains taxes, which I can avoid by donating shares.

What's my best option here?