The finders new situation is kinda lame; the IRS taxes you on the FMV of the found property which usually means that you're essentially forced to sell a bit to cover the taxes.

> Found property. If you find and keep property that doesn’t belong to you that has been lost or abandoned (treasure trove), it’s taxable to you at its fair market value in the first year it’s your undisputed possession

P. 73 [https://www.irs.gov/pub/irs-pdf/p17.pdf]

As someone who loves to just collect coins I'd be really sad to depart with any.