Power storage help

i am trying to make a 5000 btu airconditioner work with batteries and a inverter in an rv and have some questions.
i have 2 regular acid car batteries, both 1000 cranking amps or better connected in series, i have a 3000/6000 watt inverter, with the batteries at 12.7 volt it will start the compressor and run for 30 seconds and the inverter shuts down.
Im wondering if their is another battery that would be better or is it even possible or do i need like 100 batteries.

i found out that a car battery tops out around 14 volts so i charged to 13.5 and my 2 led acid batteried did in fact start and run the 5000btu unit for quite awile. so it is possible.

Now i only need to know how many amps would be to many to recharge led acid batteries over and over. I want to bring them back as fast as possible with out damageing them. 15 amps brings them back pretty fast but is that going to cause failer to the batteries if recharged alot? also i would be rechargeing when the battery at just under 12 volts so the batteries actually still have power just not enouph to use the inverter.
any info helpfull