Coyote,
That's an impressive load to have on the generator. However you might be surprised how much cooking you could do with it as well. If you loose power due to an ice storm, you will not be using the central air or the room AC, and as long as you don't dry any clothes while you're baking a cake you should easily be able use your stove/oven with it.
As to your voltage regulator, it sure does sound like a bad regulator, I assume you've checked the batteries and they are both good (no shorted plates). Running at 1800 RPM, the alternator should be putting out 30-35 volts AC. According to the TM with good batteries, the charge rate should be no more than 6.5 amps. If it is for sure your regulator, you could probably find a civi 24 volt 10 to 15 amp regulator that will work in place of the original one. I'm sure the surplus dealers have them out there, but how much they will want for one is beyond me.