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.