If you have any other pre-amp outs on your HU, you could buy another amp along with some high wattage and high SPL rating speakers for the front would help to match or overcome your loud bass. A guy at my work powered his front speakers and mounted the amp under the passenger seat. His Audi (yeah I know, not a Honda or Acura), sounds good, not to mention his custom built sub enclosures pound in the trunk.

I don't know for sure what your JVC HU can do, but on my Alpine I was able to adjust the crossovers so that I can reach the maximum volume without distortion. If your front and rear speakers are distorting before you get to full volume, and you have internal crossovers in your HU, you could try adjusting the crossovers to filter out the low end frequencies.