Yes, backing up the user partition will work. I have done an occasional factory resets so that I could reinstall firmware like you are doing. The last couple of times I have done it by backing up the user partition and restoring it later.
The only concern with this method is if the battery issues are caused by something on the user partition. It shouldn't be, but, there is a small chance it is. The only reasons I can think of for that to happen is if there was a bad book that caused lots of extra CPU usage when reading, or something causing a lot of writes to the partition. The only reason I can think of for the latter is if the database is corrupt, can't be written to properly and the firmware keeps trying to. If this was the case, then what you are doing won't work because the database will be corrupt when it is read afterwards. Doing a check on it is a good idea.
Also, make sure you get everything from the partition. There are several directories whose name start with a dot. These will be hidden on a Linux or Mac system.
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