I ended up contacting JL Audio tech support to get more detailed information about setting the sub up for optimal performance. I was told by Barry that playing speakers full range and crossing the sub at the lowest octave would result in mish mash. He indicated that the best way to do it is to cross the sub at 80 hz using an external crossover, thus freeing up the main speakers.
I think he's overstating the case. The lack of a high pass filter doesn't necessarily result in "mish mash" any more than a 2-1/2-way speaker system results in mish mash. It's the same principle at work. There are many exemplary 2-1/2-way systems in which extra woofers are brought in to reinforce an essentially 2-way speaker system without high-passing the rest of the system. Many 2-1/2-way systems are famously well blended and coherent.