Re: A proportioned size of pedal for a 18" bass drum.
Tama made a pedal for a while that came with their StageStar kits that was made for a child to play an 18" bass drum without a riser. I have never seen one up close so I can't comment on how good it is. I own one of these kits,I bought it used as a Jazz kit and It didn't come with the original hardware.
Sorry :) What you are asking for does exist though.
Rubber Duck Power Drives Me.