Lots of ideas now - excellent!
I am a big fan of simple, reliable, and cheap. Automotive parts fit this model very well. Automotive temperature sensors, relays, fans, and heat exchangers are dirt cheap compared to their industrial counterparts. In my home system most of the relays are automotive, for instance. It will take a while for my home boiler to reach 100,000 miles ;-)
Couple of other points: I come out of the aerospace world. You want to design things to fail in a safe way. If any part of my homebrew boiler controller fails, the system reverts to operating the way it did from the factory. If all the things that we're talking about were to fail, it would be good if your generator reverted to cooling itself the way it did originally as much as possible.
I love the exhaust HX idea, but I think I agree that it has to be custom fab in stainless.
Now you've got me thinking, and I don't have time just now....
How about a flat plate exchanger in series with (and upstream of) the radiator? That would protect the generator cooling system from leaks or problems. I still vote for a pair of electric fans instead of the engine fan, but I don't get a majority vote here
Perhaps an unpressurized tank with a coil of stainless exhaust pipe going through it? That way it could boil or go dry with no risk. The water from that could be pumped through radiators or whatever in the shop and/or house, perhaps via another HX coil in the tank.
Sizing all of this properly will take more math than I can deal with right now.
Keep the ideas coming....