Hi,
Just some thoughts.
Perhaps the cold start current draw is to much for your inverter. If you have a clamp ammeter you might want to measure how much current is being drawn while the saw gets up to speed.
Also when you start using it you'll of course draw more current so the voltage may fall if your inverter cann't supply the required current.
I think what also may be a problem is the supply to the inverter. All that power has to come from somewhere. If your drawing 10 amps at 120 volts then if your DC supply is 12 volts then your looking at a BIG current drain on the batteries. I would measure the DC voltage as your saw starts and see what the DC voltage falls to. It maybe that its the supply to the inverters thats causing your AC voltage to drop.
If it is then you need a bigger DC supply (ie more batteries in parallel)
Any help ?, yes no let me know.
Regards