Sounds borderline fraudulent. Be careful.

What you are proposing sounds a lot like  income tax fraud at the very least ... since  you are selling to a related party which is yourself disguised as an LLC.   Consult a tax attorney before  you do something incorrect.  

selling to your LLC is selling to yourself.  there would be no economic substance to the transaction which would result in the IRS taking the position it never took place. as others have said - see a lawyer. this doesn't pass the smell test. 

Oh boy I don't want to do anything fraudulent at all. 

Typically, a single member LLC is considered a disregarded entity by the IRS. So selling something you already own to your LLC, is basically selling to yourself. Doing that is not a recognized transaction by the IRS, regardless of the price.

Only $3000 of a capital loss can be applied against ordinary income*, in the year of the sale.   The excess is carried forward to future years.

*There is no limit on how much of the loss that can be applied against capital gains (long & short term), including  capital gains distributions.