You don't have real deep cycle batteries.
2 charged #24 batteries would be enough to run your blanket through a night: IF you get a small true sine wave inverter in the 150 watt range.
The 70 watt blanket would at most use about 60 AH which your batteries would easily be able to supply.
You need to do a lot more research on what you need. One night's not a problem, its what you plan to do in a longer term. A 1000 watt gen would be enough to recharge daily, but the batteries you have are not correct for this type of service. If you only plan to do this a dozen times a year, you're OK, if you plan to do often, you need to do a full assessment of your power needs.
Regards,
Doug