6 gauge to a 1000 watt inverter powering a 600 watt load is undersized, even if the run was very short.
Keep in mind that while one usually simply divides wattage by 12 to come up with amperage draw on a battery, one is really drawing 15 to 20% more than this due to inverter inefficiency, and the voltage under higher loads is likely in the low 11's, which means significantly more amperage is being drawn than the divide by 12.0 math would indicate. Add in the voltage drop from undersized wiring............lower voltage means higher amps which means more voltage drop. Vicious circle that can be mitigated to some degree with shorter fatter copper.
If using 6v GC-2 batteries, well they do not hold high voltages under larger loads. Their strength is repeated deep cycling ability. Those thicker denser plates of a GC2, are not designed for lots of instant high amp grunt like a high CCA starting battery.
Those wanting to power high loads from little battery capacity should go 12v AGM from Odyssey or Northstar. My Northstar, especially when new, was mind boggling in its ability to hold high voltages under high loads, like staying well above 12 volts under my 1.4 KW starter motor load.
AGM batteries have lower resistance and can support higher voltages for longer. I've never been a fan of Optima batteries as the spiral cell design knocks off ~25% of their total capacity compared to a rectangular battery, but they are pretty low resistance and can retain higher voltage when supporting high loads when still 50% or more charged. This high voltage retainment under load also translates into being able to accept higher amperages when depleted before absorption voltage is attained, at which point amps begine to taper.
A single pair of 6v GC-2 batteries are great for deep cycling under relatively light loads, but when large loads are needed to be powered, one needs them to be more than 85% charged, or needs 4 of them.
Inverters should always have short thick wiring from battery to inverter and thus be mounted nearby the batteries, but not in same compartemnt or above them.
USe AC extension cords to power distant appliances as voltage drop at 120vAC is not much of a factor, but at 11vDC certainly is.