700 watts is about 58amps, and the dual purpose battery will not last long under this load.
then there is the problem with the 700watt load on the 600watt inverter, this is much more inefficient than a 700watt load on a 1500watt inverter... the inefficiency equals higher then normal watts being used when running the heavy load on the small inverter.
you arent just burning up 700 watts that the multi cooker is using, because under a normal load, the inverter itself will use 15-17% more power just to invert the 700 watts of power needed by the cooker.... when you overload the inverter, this additional consumption can go as high as 30%.... so if you add it all up, you may be attempting to pull as much 75amps from the battery.... this is harmful to the battery and the components...
more batteries will be better in the moment, but then all the batteries will be so low it will take many hours for them to be replenished... and may even damage the batteries still, as the dual purpose batteries cant take much below a 40% discharge before it starts to degrade the internals of the battery... a true "deep cycle" battery can safely go to a 60% discharge without much strain.... but, no matter what type of battery, the batteries that get very little discharge and promptly get fully recharged, are the batteries that last many years...
so yes, as the other members said, you do need a generator for the loads you are wanting to pull thru the system.