My thoughts not based on specific experience for you application:
Plan A- put a duct to the generator head air inlet, and make a deeply folded and fiberglass covered plywood box muffler for it. A similar muffler path for the air outlet. Insulated flex duct, with a deeply bent path might be a way to do this also.
Plan B- Put the generator head outside the sound isolating box, cover most of the belt slot with a removeable plate for better sound isolation. This might not work for your frame/enclosure design but it is quite simple.
Plan C- In a book I have, one author used fully enclosed squirrel cage type blowers as a way of cooling his insulated for sound isolation diesel generator shed, which he claimed blocked the mechanical noise quite well. A pair of very small, low power ones might be worth a try. One on inlet and one on outlet; inlet might be directed to the generator head inlet.