mtrot,
You are the only one who actually knows what sort of bass attack you are talking about. Rest of us are just trying to imagine and may be completely misunderstanding and giving you wrong answers/suggestions.
"I have heard some speakers that to some extent replicate the sort of bass attack that I am talking about."Wouldn’t those speakers be a good starting point to the answer you are looking for? Many manufacturers have their "house sound" so maybe a bigger model would be just what you are searching for.
You are the only one who actually knows what sort of bass attack you are talking about. Rest of us are just trying to imagine and may be completely misunderstanding and giving you wrong answers/suggestions.