What you are describing could be considered a 'Wash Sale' and you cannot claim the losses in this case. I know for stock transactions, you cannot rebuy the stock within 30 days or it is considered a wash sale.
Wash sales aren't applicable to Bitcoin, only stocks and securities, so ignore that.
Yes, what you are suggesting is fine. If you want to claim a loss sell and buy back, however, be aware of the implications.
1) You'll lose money because of the difference in buy and sell price, as well as fees.
2) You'll reset the cost basis to that date, so if you make any gains you'll have to wait another year to get the long-term lower rates.
3) As you mention, you can only deduct up to $3,000 against any income (after reducing any other gains) per year. So if you have a $9,000 loss, it's going to take 3 years to it back.
Use
https://bitcointaxes.info, which can show you how much of a loss you would make, so you can take these figures to a tax professional for proper advice.
I don't think wash sales only apply to "securities" I am fairly certain that the rules regarding wash sales apply evenly across all assets that you must pay capital gains on.
3 is not applicable to the OP because his losses from bitcoin will be used to offset his long term capital gains as mentioned in his OP.
I personally do not think it is a good idea from a tax perspective because your capital gains were long term and are generally taxed at a rate of 20%, while your short term capital gains will be taxed at your marginal tax bracket (as high as 36%). If you use short term capital losses to reduce long term capital gains then you are essentially loosing out on the difference between the two tax brackets. It would be more beneficial if you had short term capital gains that you could offset with long term capital losses