That 600 amps is over 20 hours, not 24 hours. AH rating for deep cycle batteries = how many amps over 20 hours, to drain the battery to zero (which is bad for the battery) and car batteries are figured on 10 hours.
So, to get the battery to last for years (and not months) you only want to pull around 50%, so figure 300 amps.
Plus, as sidehack was talking about, the fully charged battery is going to be around 12.7V.
Car battery AH are figured at 20 hours also, unless that got changed in the last 5 years or so.
Reserve minutes on a car battery (and most car-sized deep-cycle batteries) is figured at a 25 amp draw.
Deep cycle batteries are expected to drain down close to zero and designed for that, normal car "starting" batteries are not.
You need more than just a buss bar to run batteries in parallel - they very enough in manufacturing that you can AND WILL drain one down while another is still nearly full charged. Current equalization is THE WAY - one way or another - for paralleling batteries.
It would be more viable to run one hashboard off one battery, the other + controller off a different battery, which would keep the draw closer to 25 amps that most car and deep-cycle batteries are designed to easily handle. Then use a proper diode isolation circuit to keep one battery from feeding off the other while feeding them all from your solar setup, something similar to what some high-end "boom car" competitors or some RVs use to have 2 batteries, one to start the vehicle (and possibly run a FEW low-power accessories) the other running the (high-power) accessories.
Low end "cheap" invertors generally put out square waves, NOT suitable for running most ATX power supplies on.
There are exceptions, many of them designed specifically for use with higher-power Solar and Wind power installations.
*ALL* "Grid-tie" inverters are designed to put out sine waves (or very close), those would be fine to power ATX power supply(ies) with.