Electronic – Estimate current draw for battery replacement

0.7 means 0.7 amps! (i.e. 700mA). I would be very worried if it was drawing 7 amps :)

You are nearly there with your calculation though: with two AA batteries in series, the total capacity is still 1800mAh. If you had it in parallel, then it would be 3600mAh (but batteries in parallel is not a good idea in general, the exception being lead acid batteris and similar, under certain conditions). So 0.7 amps with 1800mAh capacity means it would last 1.8/0.7 = 2.57 hours (2 hours and 34 minutes)

Car batteries have a high cold cranking current, as Neil says in his answer.

But they are usually a poor choice for solar storage, where deep cycle or leisure batteries are preferred - they are better able to withstand deep discharge.

If leisure batteries have a CCA (cold cranking amps) rating it is likely to be lower. They should have a max current rating instead. Or, their capacity may be stated at different discharge rates such as C/10 (which would discharge them in 10 hours). C (1 hour) and 10C (6 minutes, which may only deliver half the capacity at C/10).

C is their nominal capacity, which is often measured at a discharge rate of C/20, i.e. 5A for a 100 Ah battery.

Or the max discharge rate may be expressed as a C rate (10C) instead of a current.

Multiply this rate by the capacity to get the current.

So if you have a battery which allows 10C discharge, and you need 78A, then its capacity must be at least 7.8 Ah. And preferably several times that if you want a reasonably long battery life.