The ML's have a signature sound IMO. They are one of my favorite, even over the SVS subs.
The way to tame a cheap sub (get rid of the resonance) is to unscrew the driver, and see how much damping material you have in your cabinet. Most may not know, but the JBL E250 has none. If you were to install acoustic foam, or some type of batting to the interior surfaces, you can eliminate most of the resonance. If you were to pull a driver out of a ML sub, I'd bet most of the interior volume would be filled with some type of damping materials. Secondly, one way to overcome resonance/reverb would be to purchase a sealed enclosure (as opposed to a ported design). Sealed enclosures require many times more watts to obtain the same dB, but they tend to sound more like the ML's you demo'd. Sealed enclosures are very inefficient, but the payoffs with proper amplification are awesome - especially with music.