You didn't "break the lease" at all; you executed the self-contained termination clause. The law requires the deposit letter to be sent within 30 days of termination of the tenancy. We don't know how your lease was worded, but as a general rule, if you didn't have the right to live there, you were no longer a tenant, and the date your right of possession terminated starts the 30-day clock. So, if you paid "two months rent" in October, there is an ambiguity about when you left and how much of that was actually rent and how much was "fee" for the privilege of terminating early. When did you turn in the keys?
You CERTAINLY have a right to dispute any claim to money that you don't think you owe!
As for the paragraph on 535.300: without looking it up, that usually means that you can get your security deposit refunded in full, but still be sued for all the damage and outstanding fees, if any. The security deposit is just a way to avoid having to haul every single tenant into court every time they damage something before they leave.
However, you say they claim $704 for "carpet replacement." How on earth did you damage their carpet? If you did not damage the carpet (which they have to prove you did), then they cannot bill you for it, let alone seize your deposit or sue you for it. It is generally the landlord's expense to replace carpet if it is "ordinary wear and tear". Even if you damaged the carpet, they can only charge you for the value of the carpet you actually damaged, not the cost of a new replacement carpet for the whole room! So, if the carpet was ten years old, the value of replacing that carpet with a 10-year-old carpet is approximately zero, because the old carpet was due to be replace by the landlord ANYWAY and they cannot claim it was damaged and simply send you the bill or seize your security deposit (assuming they did it within the required 30 days, which is questioned above).
Advice? Letter to the landlord, "I object to your claim to my security deposit for the following reasons: it was not delivered to me within the allowed 30 days from termination of my tenancy, it did not include any proof that I caused any damage, and it did not contain any proof that it actually cost you $704 to repair any damage that you allege I may have caused. Please refund my entire security deposit immediately." Send certified mail, return receipt. Hire a lawyer to deal with it if they get nasty.
You have a right to itemize the bill to the exact cost and to question the cost. You or he can go to small claims court to dispute the matter if you think he is over charging you. He has your deposit, so you will need to sue him. My best advice for you is to ask for the itemized bill and see if it is reasonable. If you go to court and want an attorney to represent you, that may cost more than $704. You could represent yourself, especially if he doesn't provide and itemized list. I would question if someone else was in that apartment from Oct to January. If so, you have a better case. 3 months is very unreasonable for the landlord to have a carpet replaced and repair other damages, especially if he used professional services.
I once had to sue my landlord for my deposit back and I won. I moved out because the refrigerator broke and had a baby. I moved out 2 months after it wasn't fixed. Then after 3 months the water broke. He tried to stick me for the water damage. We settled out of court. I came out a head because he refused to give any of my deposit make and I received the whole thing. I did have an attorney; however, he didn't charge me. I still owe him big!
Good luck.