Good sound isolator/deadener applied directly to the inside of the compartment will go a long way to eliminating sound. Specialized for car firewalls and hoods is the way to go as those are heat, oil and gas resistant and are nearly permanent bond to the surface it's applied to.
I would then get a set of engine mount isolators to bolt onto the bottom of the Honda to help. These are thick heavy rubber made to isolate vibration. A good alternative is isolators made for air compressors, some you have to watch for oil/gas resistance, but they are designed for vibration isolation.
The set of compressor isolators only cost $15 bucks and one pair replaced all 4 of the existing feet of my portable generator - made a big difference.
All of these items are available from a good auto parts supply house. There are some pretty thick mats available to absorb and deaden the sound and vibrations.