Your post is very unclear as to exit deal LL has offered. --- refund just what balance
But if the offer is to refund your deposit in full and refund you for 3 months remaining on your lease , then I too suggest you are wise to accept her offer --and I'd accept it in writing pronto so as to lock it in!
Her offer far exceeds what I think your practical options are under the law if you chose to pay the game some other way ...
If your deposit is 1 month I read your post in context of she is offering about 4 months cash to vacate ??
You accept an offer by accepting it exactly as made --any changes pretty much cancels it out and make your deal a new counter offer .
(Me, just me, I'd clearly state the terms of her offer in my acceptance just so the details do not get lost if it was an oral offer.)
I'd not make the details of cash for keys into a new offer and if you want to tough it out for a few days/week with electric heaters I'd keep that separate.too.
I think her offer is overgenerous relative to the likely costs of fixing it and once you depart she is still stuck with problem and no cash flow --and once she wises up she may take her offer off the table --but if she made an overgenerous offer and you locked it in via a delivered written acceptance --so be it.