Yeah I've thought about an inverter, but 1500 watts is 125 amps @ 12v before you add in for overhead. I have a 4 golf cart house bank that are paralleled thru a battery switch. I imagine it would require a serious re-wire of my batteries with massive cables to support that kind of current draw as an inverter would be several feet away from the batteries at best. Also an inverter just adds another piece of equipment, adding to overall boat complexity. I like to keep things simple on my boat. Getting a 2K generator just replaces the 500W that I have, so other than the slightly larger size it doesn't really complicate things.
And if she runs the dryer for 6 minutes that's 12.5 amp hours out of the battery before overhead. Probably translates to another 40 minutes of run time with the small generator to replace this. So 6 minutes of a louder noise or 40 minutes of ongoing lower level noise. The time frame's not really a problem, showers for seem to end up in the late afternoon anyway, and that's when the sun shower is hot.
I suppose I could be persuaded to revisit an inverter, I'll look into it further before I buy a new generator.