If you are audited, write them a letter and tell them the exact same story.
The bank will not issue a 1098 with your name and SSN on it until the assumption, so deduct the interest and check the box for "this interest was not reported on a 1098."
Under the normal IRS rules, only someone who is an owner (listed on the deed), and obligated on the mortgage, and pays the interest, can deduct the interest. In some circumstances, a person who is not obligated on the mortgage document can still deduct the interest they pay, if they meet certain tests for "equitable ownership". Your problem is going to come more from the fact that you put money into his account to pay the mortgage, and less from the ownership issue.
For November and December, you legally own the house (even if the deed has not been updated with the county clerk yet) and you paid the money from your own account, so you are allowed to deduct the interest, even if the loan is not in your name.
For March to October, you legally own the house, but your father (or his estate) appears to have made the loan payments. (This was a mistake on your part and you should have immediately frozen his account and sent the bank checks from your account.) You can deduct the interest if you can prove you made the payments. You will need to have documents showing that his bank account lacked sufficient funds, and that all the funds used to pay the mortgage came from you. This will be tricky and there is a possibility the deduction will be denied, but it is what it is.
For January and February, when your father was alive, you can deduct that interest if you paid it and if you can make an argument about equitable ownership. Did you pay in January by the same transfer method or did your father use his funds? If he was paying the bills before the nursing home sucked up his money, then you did not pay January and can not deduct it. If you did pay the January mortgage payment then we have to move to the question of equitable ownership. Did your father put your name on the deed to the house? If not, then during the time you lived there, did you expect to inherit the house and did you act like an owner? Did you perform repairs and maintenance? Did you and your father tell friends and family that you were going to inherit the house? Did he have a will that made this clear?
In the end, it sounds like you are entitled to claim either 10 or 11 or 12 months of interest, depending on which months were paid with your funds, and whether you have a good argument for equitable ownership before he died. You would claim the interest on your tax return and check the box for "I did not receive a 1098." If you are audited, your response will be documentation of all the things I just discussed (proof of his bank balances and bank transfers, copy of his will, other information proving equitable ownership, etc.)
Here is a good article that discusses equitable ownership.
http://www.forbes.com/sites/anthonynitti/2014/12/30/five-traps-to-avoid-when-deducting-mortgage-inte...
