Real Estate Law
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To be very honest with you, while their number might be a bit on the low side, it is probably close enough to be reasonable, especially if you had some use of the property and didn't stay in a hotel for that entire time. Basically the courts look at what the reduced value of the dwelling is without AC vs with. So if it was worth $100 a day with AC, a judge might find it was worth $50 without. But he isn't going to say it is worth $0 if you were actually still using it or occupying it.
So you could probably goose them up a bit more and tell them that you will settle for $1200 as a credit or you will file suit in small claims court and try your chances there. It will cost them well over the $300 extra you are asking for to hire an attorney to represent them in court if you sued, so they should agree.