I do want to make some things clear for the OP.
-The Kappa Perfects, in proper ported caibnets, will easily out perform even the 13W7 in the lowest octave, by more than 2x the output, if comparing the JL in a sealed cabinet. The problem is the cabinet system. You can not buy a pre-fabbed cabinet system for this; the port and cabinet have to be custom/specially designed/built to get proper compression free performance from this driver.
-The JL 12W7 is using brute force to make up for lack of proper ported system. It's extreme linear excursion(this is critical/ that excursion is linear - most drivers are no linear) and power handling allow it to make up the small sealed system. You MUST feed about 2000 watts to each driver for this method to work as intended for high dynamic range and distortion free sound.
-The AXIS drivers are incredible, being roughly equivalent to the W7s, but you would be paying much more for the AXIS drivers because you can get W7s about 100 bucks cheaper to begin with (comparing 12" versions of each), and then you have that Microsoft live.com 25 percent discount you can use on top of this. In the end, you could be able to get a 12W7 for about 400 shipped roughly after the live.com cashback.
If you went with a pair of the 12W7 set up as I recommend(dual Ep2500, DCX2496 controller), the total cost for this would be about $1900 USD. The retail F112 JL home version using a 12W7 is over $2000 USD each. So a pair wold be $4000+ and you would have less processing/xover power because the DCX is far more capable then the limited built in processing on the retail units. In addition, you would likey have more actual power/output with the DIY version. It is simply unlikely that the built in JL amps match an EP2500 in real world use. JL amps give power rating in 'shor term dynamic' conditions, please note this. The EP2500 amps provides more power in continous RMS output than the JL Fathom F112 amp provides in short term dynamic. The EP2500's 'dynamic short term' would of course be far higher than the continuous output. The JL 12 W7 can safely hand the Ep2500 with no risk of over heating the voice coil. The W7s have extremely robust design and are among some of the best woofers in the world based upon objective measurement/analysis.
Please note that as wit ANY high powered sub, you need to provide dedicated circuits to them for maximum performance potential. Of course, in real use, you won't likely use but a few tens of watts for music. The only time substantial power is really used is in the occoasional extrme dynamic LF effect in movies and if you purposely turn the subs up to show off.
-Chris