It will be expensive and difficult to do what you propose to power an inverter from a large frame alternator underway.
You will need a big alternator, an external regulator and an engine mounting system. You can certainly install a 200+ amp alternator that will do what you want. Even at trolling speeds- 1,000 rpm, this alternator will put out enough at 2.5:1 pulley ratio to do the job:
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But why not install a $300-800 bus heater and connect it to your boat's cooling system to give you heat undeway. Heatercraft makes them in all sizes.
David