The landlord's recharacterization of the "last month's rent" as part of the "security deposit" can be challenged by principles of contract interpretation, but it's not feasible to give you the best advice based upon the limited disclosures available in a forum like this. Suppose you just tell the landlord that you've already paid for the final month and you're not paying more. What will the landlord do? If the landlord is gutsy, the landlord will give you a 3-day notice to pay or vacate, and could try to evict if you don't comply. I tend to think you'd win, but you don't want your name associated with an eviction case in a public record even if you do win. If the landlord tries to blacklist you in future tenant screenings or credit reports, you might have a reasonable claim for relief under the federal Fair Credit Reporting Act and the state counterpart of that Act, but the stress, risk, time commitment, and maybe attorney fees would fall mainly on you, at least in the beginning. If you can come up with the money, the most conservative way to handle it is to go ahead and pay the rent and then come down the landlord's throat hard if -- when -- you don't get the security deposit back promptly, or an accounting for why not. The money or the accounting must be mailed to you within 14 days after your move-out, to your new address. It would be interesting to see if the landlord is willing to tolerate scrutiny of his/her trust account where the security deposit is supposed to be held. If you can't come up with the money for the final rent, you have what I'd call a good argument that your security deposit was intended to cover the final rent. The security deposit clause was written by the landlord, and apparently imposed upon you at the last minute when it was too late for you to change your plans, and that means that any ambiguity in the meaning of the security deposit will be construed in your favor. This would be fun for lawyers to litigate about, probably not so fun for you. Many, maybe most, pre-printed lease forms contain a clause to the effect that what's on this paper is the whole agreement and nothing else matters, which is a clause intended to make your pre-occupancy email exchange irrelevant. There are legal principles for getting around that clause, but it means a potential legal battle. If the landlord did not keep the money in a trust account, your argument will be stronger. This comes down to your tolerance for risk. My evaluation of your situation, or any lawyer's evaluation, may be much different after all the facts and records of your transaction are known, not merely the summary in your posted question.
This answer is intended as a courtesy only, and does not constitute an attorney-client relationship between the attorney and the questioner.