Of course this speaker exists...100's of times over. I think you can find any number of tall slim tower designs with several small woofers to fit the bill...obviously it will need to be ported or double ported to get that bass extension you desire.
Your requirments are pretty much main stream sweet spot; a reasonably priced, good looking, unobtrusive furniture piece with impressive but slightly warm sound.
If you wanted something with dynamics, accuracy and low distortion levels then my answer would be different.
As for 18 inch from the back wall....you will unavoidably get some rear wall comb filtering (quarter wave cancellation) in the bass from any speaker you choose, which means some notes will suck out worse than others (this can be reduced by placing the speakers much further out into the room)