You are also not taking into consideration the effect of the batteries sitting for most of a year. Any lead acid battery will sulfate when left sitting for long periods of time. The only real option for this type of use is a Lithium Ion battery. Also your AH calculations are not correct. If you put 2 batteries in series you do not gain AH, you gain voltage. When batteries are put in parallel you gain AH not voltage. So if you put 2 12 volt batteries that are 100 AH in parallel you get 12 volt 200 AH. If the same batteries are put in series, you get 24 volt 100AH.