There's a pretty simple solution: Abolish the capital gains tax, and tax all capital gains at the income tax rate. There is no more "capital gain". Only income. Whether your income was earned through labor or rents on capital that you own seems rather irrelevant to me.
Let's think about secondary effects. What percent of very wealthy Americans do you think would renounce their citizenship based on this? How much less investment capital would there be in the USA based on that? Note: Not asking for a value judgment ("good riddance if they do!" - not productive). Just your estimate as to what percent of wealthy Americans would give up their citizenship and how much less investment cap…
I wonder if it would be a wash, you suddenly up the tax, and everyone that was ducking anyway leaves and the rest get taxed and fill the void.
All speculation of course, none of us would have numbers to know.