I think your on the right track with what the cars use.
They do make a soundproofing product that you attach it form the underside of the engine compartment. I sure if you google this you can find all sorts. Check Overton's or West Marine.
West Marine has it called Noise Control Barrier Material. A 32"x 54" 1/2 thick piece is $112.99 and to go 1" thick is $154.99 included tape and hanger kit
Keep the cost down by DIY.......looks like an easy project.