It isn't cheap, but I'd replace the vent fan with a Fantastic Vent, one that has a rain sensor, or ideally, a MaxxAir fan that works with a vent cover on it.
Then, open a few windows, set the fan's thermostat, and let it do the rest. To keep it powered, one can plug the van into shore power, or see about adding a solar panel or two to offset the amp draw of the fan. One benefit of a solar panel is that, due to the air gap between it and the vehicle, it provides shade.
Of course, the ideal solution is a carport, but a high flow vent fan can help.