Self-directed IRA seems suuuuuuper iffy. You have any support for that being an acceptable position for someone to take without realizing the potential risks of getting audited? To my knowledge, the IRS does not agree with you that Bitcoins can be deposited into an IRA or purchased with an IRA. Not saying its disallowed, but if so provide proof please.

LLC = make sure not to use this model if you plan on mining. S-corp. allows you to avoid self-employment tax that would be unavoidable for LLC mining business (because mining is a service and partnerships must pay self-employment tax on service income). Also, an S-Corp might be better, if a little bit more complicated. I prefer the S-Corp model but do your own research. S-Corp provides the main benefit of the LLC in that you're entitled to flow-through profits and losses.

For a better idea of the issues, talk to a lawyer who specializes in the field. Otherwise, pay your tax. You don't want to be wrong on this one because the penalties are going to be draconian if you fail to report / underreport and get caught. Playing the audit lottery is unwise.