The most ideal solution is to enclose the power supplies and amps in an entirely sealed dustproof chassis. That may require beefing up the heat sinks and getting them on the outside of the box if there is a way to keep the MOSFETs inside the box. Ditto the power supply. It would be a good idea to ask someone on a forum how hot the inductor and RC network on the output filter get at full power. If there is heat there, no idea how you would get rid of it in a sealed box. A D is going to produce less heat by principle than an A, B, AB, etc. So that is good.
Same with the power supply, what gets hot when the amp is running at full power?
It would be cool to run some kind of air to air or air to water heat exchanger for fun. Of course dust could corrode. Aluminum NEMA waterproof enclosures would be dustproof. The RF ones are steampunk. Surplus or catalog items. See pic.
Or since they are cheap, you could let them get dusty, try to wash them after, first with a light acid, then water. If there are protection relays, those may not wash.
Generator power is extremely crappy. Running off a battery would be ideal, even if through an inverter. If running off a generator, no idea how hardened the power supplies are against spikes. People run commercial class D's off generators all the time though.
Obviously keep the amp in the shade.