I only read some of the responses here and quit some ways down as many folks seem to be missing key points here. Including you OP.
A) As of November 2016 - tenant still has possession of property
B) A notice of rental increase, many months ahead, is not a breach of contract
C) Abandonment loss does not occur until the property is vacated by a tenant
D) As a Landlord you are not responding to this tenant correctly
The current contract which details the lease of the property and the current rent which is good through June 2017 prevails. Giving notice of a price increase 7 months ahead of time is absolutely not a breach by the landlord in the covenants of a rental agreement. Had you attempted to apply that rental increase to this active contract, that would be a different story. But you didn't so let's not go there.
Presumably, the current lease agreement states the tenant is responsible for any loss if they breach the contract which includes abandonment and voluntary surrender. To be clear, the tenant is voluntarily surrendering the property. When you told them you would raise the rents and they said they would leave you should have also made it very clear, they are financially responsible for the total amount due until the lease terminates or you find a replacement renter. There is a sense that some degree of this idea is being kicked around by the tenant and the OP but to what explicit degree is not clear.
As the landlord, you are not obligated to pro-actively seek a rental replacement until after they vacate. The condition of the property when they vacate is unknown until such time as they vacate. The property may not be rent-able and as the landlord you must regain possession prior to being able to offer the property back out to another renter. Again, right now, November 2016, the tenant has possession of the property.
As the landlord, you do not owe the tenant any list of actions or responses on their demands. He/she is just being ridiculous. On top of that, they misread the statute.
I would respond to the above email reminding he/she that they are not in any way obligated to terminate the lease early. By terminating the lease early, they are creating a financial hardship onto you in having to spend the resources and time to find a new renter. Their vacating the property will force you to seek all legal remedies during the time rent is not paid per the contract. Per the lease agreement and state law the tenant is obligated for the full term of the lease and all payments.
Once they vacate, if they do, then you can inspect the property and make it rent ready again. The tenant would likely, per your lease agreement, surrender their deposit, if any, for breach of lease. You can use that against any repairs and rents due until you find a new renter.
As a landlord you have no obligation to advertise for a renter prior to their vacating. You have no explicit timeline as to finding a replacement renter. You have no explicit requirement in how you search for a replacement tenant. Let us assume, with a dash of common sense, it is in your best interest to rent the property as soon as you can, because, well, you know,....money. Once that rental agreement is executed, the day before the first day of possession granted to that new renter is when the previous (vacating) renter is relieved of their obligation under the current agreement. (You can't collect what would be double rents)
I would tender a letter to the current occupant which outlines these ideas and clauses from your rental contract. I would also include a total amount due under the terms of the lease from December 2016 until lease term. I would note that the property will be inspected by you and provided there is no damage, the security deposit will be applied to unpaid rent. I would cordially inform them via the same letter you will, per statute, seek a new renter but they will be responsible for any and all unpaid rents and fees per the agreement. Sorry to see you go and all that nice stuff.
I wouldn't engage any other type of correspondence or conversation. When you have it rented, make your final payment demand and give them time to cure. If they do not, file in court for your unpaid rent and fees - if it is worth it.
Next time, don't let the tenant turn this into a circus. Good luck.