A possible solution, in that the coins value is based only on their scarcity. The legitimate conditions of purchase and how they originally got out seems to also be an issue, as I did not find any reference to the fact they ever proved, through hard evidence, that the guy actually smuggled them out. Even then, smuggled or not, were they not still legal tender? Did the Fed Reserve act ban them? I know there was a bunch of them found in California a while back that never heard from again, but speculation was they may have been the missing ones. You are correct in how the Fed is just legalized smoke and mirrors.

Absolute power corrupts absolutely.
The solution is to repeal the federal reserve act and all the actions done under color of law e.g., executive orders of FDR, and to reissue double eagles as US money.
As for the specific coins and their ownership, the feds have already compromised with a previous coin owner and in so doing, set a precedent. They should treat these coin owners the same way by negotiating a sale price in near worthless paper currency at gunpoint. Of course, not having possession of the coins will likely affect the market price in the estimation of looters.
Supreme Court appeal? Waste of effort. They are at least as corrupt as the rest of the federal government. Expecting a federal judge to rule against the feds is foolish.