I'm starting to wonder if you guys even know the amp you're so proud of....
First, look at the RF literature. The Hybrid Technology is predominantly described as a current-averaging system. In case the diction doesn't make it clear, the T15K draws less peak current by drawing more current during low output, which is then stored in the capacitors for use during high output.
As already noted, the T15K does not have efficiency greater than 100%. Power (energy over time) output cannot exceed power input. During low demand, the amplifier actually has a negative efficiency (relative to output). The energy stored in the capacitors during this period means you get extremely high efficiency during high demand periods (relative to output). However, this efficiency cannot be sustained...and should not be specified with the continuous ratings. What you are looking at is 15kW of output for short bursts, not continuous tones. How it got CEA-2006 rated is beyond me...
I doubt math will help others, because they're obviously already ignoring it, but we'll try anyway...
If the battery only supplies as much as 350 amps at 14.4 V, the power from the battery is 5040 watts. If we assume AB efficiency of 80% (generous), you're looking at a little over 4000 watts output provided by from the battery. So where's the rest of that energy coming from.....?
We know the amp uses a large bank of capacitors. RF has mentioned in the past that it offers 225,000 joules. The roughly 11,000 watts remaining (to achieve the published 15,000 watt rating), all of which must go through a class AB output stage. Again, assuming 80% efficiency, you're looking at 14,000 watts input to achieve the remaining 11,000 watts output.
So, coming back to the 225,000 joules. A joule is a watt-second. Taking 225,000 joules and dividing it by 14,000 watts, you're looking at ~16 seconds of continuous output at that level.
And guess what happens once the capacitor bank is drained....you need to start filling it back up. To charge the 225,000 joules worth of capacitors back up, you know again that we can't supply anymore than 4000 watts (per RF's own literature, ie. the 350 max amps of current draw...see math above). Take 225,000 joules (or watt-second) and divide by 4000 watts....it will take approximately 56 seconds of continuous 350 amp current draw just to charge the capacitor bank again!
In reality, what you have is an amplifier that can do 4 kW continuous, and supply 15,000 kW peak for short bursts. Oddly enough, most people normally object to companies that rate products like RF has here....