L;
Wire sizing for battery draws can be confusing when there is an inverter involved.
An inverter is a constant Wattage device where the Watts drawn from the battery are determined by the 110VAC appliance making the draw. What happens is that battery Volts drop and Amps rise over time. Both of these factors dictate wire size and both are changing in opposite directions.
Using your cooker's 580W draw, let's see why your inverter is alarming. With a 10.5V low Volts alarm, your inverter is saying it can't get 580/10.5 = 55Amps input. That is the worst case ignoring any alternator contribution.
Alarm situation - Voltage drop percentage: 3.73%.
Shorten the wire to 16"(1.33').
Voltage drop percentage: 0.33%.
If you draw the full 2000W with 4Ga, 2000W/11V:
Voltage drop percentage: 1.09%.
Here is mine at 1000W/11V 2/0Ga 3.5' one-way:
Voltage drop percentage: 0.45%.
Try another test with best case 14.4V as you might see with the alternator where Amps would be 580/14.4 = 40A.
Since cables are a one-time cost there is good reason to go for lowest loss% in worst case situations.
HTH;
John