Awesome work, Ian.
A detailed how to of this would help a lot of folks in similar situations to yours I'd bet.
Wonder if a copper tube, liquid, fan arrangement...like a laptop uses, could be workable.
I can draw a schematic easily enough, but how to physically convert the alternator depends heavily on the particular brand and model used.
HD diesel truck alternators are the way to go, particularly if you aren't an electronics god who can build complex and efficient circuitry and timers to control the output as a pwm square wave. For hulk-smash types like me who know just enough to be a danger to themselves and others, I would recommend using a Leece-Neeville wye-wound alternator because the three phase outputs are already external, all you do is pull the regulator off and bolt a piece of plexiglass in its place and put two brass machine screws for pass-through studs and hook the brush wires to them on the back side. Then you get one of the three-phase rectifiers from Amazon (get the 400 amp one instead of the 200 amp one that I did, $60 vs. $33, I went cheap on the first one because I anticipated frying it with voltage spikes). Get a good aluminum heat sink and fan to go with it, or rig a liquid cooling system and pump. Cooling the rectifier was my biggest problem and I still haven't solved it in a convenient way. You could also get a 400 amp 3 phase air cooled rectifier already made up for $150 from one of the online alternator parts superstores and just hook the three inputs up direct to the Leece-Neeville's outputs and hook your welding leads straight to the big brass DC output studs on the rectifier assembly's lid. Then all you do is run fused, switched 12 volts to the rectifier cooling fan and 12 volts and ground to the alternator field with a 5-ohm rheostat and 7.5 amp fuse on the hot side, and you're ready to weld. Well, after you figure out how you're going to drive the thing at 8-10,000 rpm (prolly 15 hp) and regulate the speed and field voltage remotely.
As an on-board welder for trail repairs it would actually save weight and headaches to carry a second battery and some connections and short welding leads so you could weld anything on your vehicle without the engine running, just pull the engine battery and hook it in series with the spare. Or do what you do now and use the spool gun. For a portable farm/ranch/shop welder it makes much more sense to use a riding mower engine (or the whole mower less the deck) and not worry about adding an additional system permanently to a vehicle. The problem of throttle control, rpm governor, and small charging system are already solved with a small engine system like big riding mower has. If you use the whole mower, the problem of transporting it around the homestead is also solved.
I don't have a riding mower or know of one I can easily get, and didnt have any junk Leece-neeville alternators to use. I had my old pickup that doesn't get used for much around here and a barrel full of Delco-Remy 22 SI alternators, so this was the cheapest way for me to test the idea and see if it was worth the trouble and money to do it right. After using the system I cobbled together, I'd say most definitely worthwile to build one even if you have to buy some of the major components new.
I have about $55 in copper lugs, heat shrink tubing, 8-gauge wire, electrical tape, and the 200-amp rectifier. Everything else was salvaged junk, old second-hand cables, or leftover scrap. The chepest offshore engine-driven welders I found new started at about $1200. Renting one is about $250/weekend here. The Premier onboard welder starts at about $1400. Doing this from scratch only makes sense if you have a lot of the stuff like welding cables and a powerplant already.