Unfortunately yours in the wrong approach for any of the EU series inverter gensets which were designed very carefully by Honda engineers to use the genset case itself to draw in cool intake air while simultaneously keeping it separate from hot cooling air and hot exhaust gas which both need to be vented out. I built my own
EU2000i Quiet Box around these principles which also apply to the EU3000i. Alternately you could modify your EU3000i by replacing it's exhaust bezel with this custom design from
Generator Line which will allow you build a proper sound enclosure box that
will keep these various gases separated, as intended by Honda engineers.