Battery support capacity for inverter supply of 30A over 3hrs
$$P = V \cdot I = 120 V \cdot 30 A = 3,600 W = 3.6 kW$$

You're looking for a 4 kW UPS with 3-hour uptime. (I've ignored the reduction to 20 A to give some margin for deterioration of batteries over time.)

Have a look at readymade UPS solutions before you try to roll your own. You'll find all sorts of benefits from reliability, self monitoring, alarms, automatic mains switchover (if mains is available), stable frequency and voltage, etc. As the UPS manufacturers purchase batteries in bulk you may find a readymade solution at lower cost than purchasing components and building your own.