The industry adopted a 14.4V input voltage standard for measuring power output. The problem is, a vehicle's electical system is 12.5V not 14.4V. So basically, most amplifers (yours and what was recommended) will not produce the rated power once installed into your Jeep. For every 2 Volts change in input voltage there is a 30% change in output power. Your amplifier is producing about 240 Watts RMS if that 360W is an RMS rating and if its a "Peak" rating (completely useless) its producing about 120 Watts RMS in your Jeep.
That being said, you have to consider your goals and how to get there.
Physics is a biznatch-goddess: it takes alot to get a little.
When listening to music it takes a minimum +/- 3dB change to dectect the difference. This means if the change was +/- 2.5 dB you would not notice the change.
If you want to increase output by +3dB you need to DOUBLE the power you currently have. To get to the next noticable increase (another 3dB) you need to double power again (From 120 Watts to 240 Watts to 480 Watts). Can your woofer handle that? Remember, the music is only 3dB (one click of the volume knob) louder but the voice coil is not getting twice as hot.
Physics is a biznatch-goddess: it takes alot to get a little.
Now that we are getting our minimal 3dB gain and the voice coil is getting hotter a new scenario creeps in:
Thermal Compression. As the voice coil gets hotter, its impedance (frequency dependant resistance) increases. As impedance rises, it's harder for the amplifier to produce full power anymore and the output goes down. So you just bought a new amp and your only getting 1 or 2dB increase which you can't hear because the woofer is getting too hot.
Physics is a biznatch-goddess: it takes alot to get a little.
Now you try to get your money's worth in output. So you keep turning it up more and more. The impedance of the driver rises higher and higher and the voice coil gets hotter and hotter so the amp produces less and less. Eventually, the woofer is destroyed.
Physics is a biznatch-goddess: it takes alot to get a little.
There are two ways to increase output: increase power and/or displacement. Since there's no replacement for displacement, I recommend starting there. By doubling displacement you can gain 3dB as well. Add another 12" woofer and you'll get another 3dB without changing the amp. If you take advantage of the fact that you power handling has now doubled and add another 120 Watt amp, you now have +6dB of output potential. This would be a very good increase as well as being safe for the woofers. If you were to go from two 12" subwoofers in a sealed enclosure to two 12" subwoofers in a ported enclosure, you'll also get another 3dB. Do all of this and the potential is a 9dB boost.
A deciBel is 1/10th of a Bel. A Bel (+/- 10dB) is a measure of twice of half as loud. If you do all the above stuff, you will not have much cargo area left, but you are going to be nearly twice as loud.
I tried to find specs for Quantum subwoofers but there was nothing useful on their website.
If you are in the market for a new amp look to companies who are being honest about their numbers. As I wrote earlier, the 14.V numbers (CEA 2006 standard) are not honest at all for use in a 12.5 Volt system. There are few campanies who still rated power at 12.5V input, I can tell you that JL Audio is one of them.
As you go out into the world seeking to add displacement to get more output people (in forums and professionals) will tell you that you can destroy the woofer if you "underpower" them. This is BS and it's a myth that has been around for a long time. If this were true, you would have to play you system at full volume all the time so the woofers would not blow up. How many people do you know blew their woofers by turning the volume down (under powered)?
Good luck in your quest for morre boom.