Not trying to start an argument, but a hydraulic driven generator would be the least efficient of all.

Generators will require 2 HP on the shaft per KW of output. The problem is building a drive that can handle the torque and give the proper shaft speed. Most generators in the 3 KW range are wound to run 3600 RPM to give the 60 HZ You need. This means You will need large diameter pulleys on the engine, as it is only turning 1500 RPM.

An inverter supplying 1800 watts [15 amps @ 120V] will draw 180 amps at 12 volts. While the battery will provide enough power for short perids of grinding, continuous use of a powerfull appliance will soon drain the battery.

There is NO WAY that the high output alternators will provide their rated output at welding RPMs as they are rated at MUCH HIGHER shaft speeds [frequently 6,000 RPM]. To get full output, You will need to drive it with a greatly oversize pulley on the engine.

For heat aplications, consider heat lamps, or a coil heater that has no fan, as they can run from the DC Aux. power on the machine.

Ok I'm writing it in my little black book... If Kaye comes to Sunny Az for a cruise on the boat, BEER only!!! for the first day at least.lol

Down in the islands We called those "Hurricane Blenders" as You can keep the hurricane party going after the power goes off.
Good for islands with no power too.

Actually you can do that.  When adding extra batteries though for inverters to run appliances and power tools on though it's a good idea to use a battery isolator for the extra battery.  The battery isolator lets you use one high amp alternator to charge all your batteries.  If the one battery on the inverter or other high amp pulling accessories pulls down you still have the other battery charged that only runs your starter, lights, and vehicle ignition and accessories without pulling down both batteries that way.  Ambulances, fire trucks, over the road trucks have been using battery isolators to do that for years now it's nothing new and does work well.  Get a isolator that is rated a bit more than your alternator amps and the load you want to run on it.   

http://www.colehersee.com/04resource/tec%5EBatt%20iso.htm

You probably don't need a alternator with 250 to 300 amps but they are out there and not cheap.  An emergency vehicle with all those high amp flashing lights, cordless chargers, inverter, and other high amp drawing accesories won't work on one battery and a pissy ant 50 amp alternator. 

http://www.nationsautoelectric.com/ecotech.html

I have my truck batteries as well as my SA250 batteries wired into my 3500 watt inverter. It works very well. I like the fact that if I need power for a small task I dont have to cranck my machine to get it done. I've also noticed that my machine does not drag when cranking for the first time on a cold morning. I assume this is do to the truck keeping a full charge on the machine.

I've had my SA 200 hook to my truck battieres for years. It works great and I never have to worry about it starting in cold weather. I dont even have a battery in my welder.

ive seriously considered buying a little trailblazer just for their 10000 watt ac power, plus i could get one with ac weld output and have the ability to tig alum in the field, with a hi freq box.  It could also serve as a backup just to get a job done incase my sa250 took a crap.