Can't help you on calculating the current density (although there were some other threads on that topic here at eng-tips about a year ago).
But here's some benchmarks for copper you can compare to if this helps (all at LV, 12 to 480 volts):
Many switchboards I've seen seem to rate 6x0.25" bars (1.5 sq. in.) at 1000 or 1200 amps, that'd be ~670 to 800 amps per square inch.
Many specs that I've seen for panelboards seem to require a bus rating based on a maximum of 1000 amps per square inch.
In one of those other posts I mentioned, the idea was discussed of painting the bus black to increase heat dissipation. Interesting idea, but one I've never seen done.
Conversely, insulation or other bus covering would seem to lower the ampacity.
Bare copper should be able to take pretty high temperatures OK -- so I'd guess the limiting factor is the heat rating of the bus support, the ability of the joints to perform at a given current density, device terminal temperature ratings, etc.
Hope that helps. There's probably others here that could give you better answers.
One more thought -- the generator vendor is probably the only one that could give you a precise answer for your situation if UL or similar listings are an issue. Why don't you ask them?