What if you gamble it first
As long as the casino doesn't ask where it came from or care... however casinos are usually heavily scrutinized.
Just look for a game with 100% chance to win, there are many. Of course, you lose the house edge, usually 1% to 2% depending on the operator. Many dice games don't allow setting a 100% chance to win, so you'll have to decide if 99% chance to win is good for your bitcoins (or put another way, if 1% chance to lose is acceptable to you.)
The loan idea is better, and it's "cleaner". The idea from the chapter of the book I'm talking about (it's on the internet somewhere, for free) talks about forming two corporations. A US based corporation and the Offshore based corporation. The US corp borrows. The Offshore corp lends. The US corp never pays back the loan, but that's between the two corporations. Or they can come up with a legal thingie that implies the US corp can pay anytime when able; but they never do. Or some absure number of years, like 200 years at zero percent interest. Or negative interest.
Accountants are also good at this kind of thing.
So, in this scenario, one would continue living in the US, collecting a $99,999 salary from a foreign corporation, and paying no taxes anywhere?
I believe the idea is for the US citizen to live and collect income in the foreign country. While remaining a US citizen. If he renounces citizenship, that's another story and has its own complications.
After having had a permanent resident visa for a long time (of the US), also known as a "green card", I'm about ready to give it up or abandon it. I'll just visit. I haven't lived there in 20 years anyway.
Here are a few other countries OP may want to investigate:
Belgium
Malaysia
New Zealand
Belize
Hong Kong
Cyprus
Barbados
Isle of Man
Jamaica
Sierra Leone
Sri Lanka
All of them do not have capital gains tax. Someone please correct me if I am mistaken on any of them.