Powered woofers almost always feature equalization and permit other adjustments, allowing adjustment to woofer output, crossover points, phase and even crossover slopes on some models. In addition, more and more of them use Class D circuits (frequently, the ICe module), which seem particularly adept at controlling woofer cones. Thus, despite all the cubic feet you have, four 15" drivers move a lot of air and, assuming the powered woofers do feature equalization, you will definitely benefit from the adjustability they will allow.
As for standard amplifiers, even very high powered ones, they offer no adjustability and the only means to vary woofer output will be through varying the location of the speakers in the room and by using room treatment.
More importantly, if you do not have to worry about powering the woofers, you can choose an amplifier of low to moderate power to drive the midrange and tweeter drivers. Because of the many transistors in the case of a high-powered solid-state amp or all of the tubes in the case of a high powered tube amp, high-powered amps tend to lack transparency and "magic" compared to lower powered amps. As an example, one of the reasons the darTZeel amp is so good is because each channel uses only a single pair of transistors. In short, if you have very power-hungry speakers, then a big amp becomes a necessity, but if you have the luxury of not needing a lot of power, you can go with a much smaller amp that will have superior resolution and finesse (among other advantages: a smaller amp uses less electricity, has fewer parts to break, is generally less expensive to buy and is easier to resell if you decide to sell it).
At the end of the day, listen to Ty, as he is the expert regarding his speakers and he will want you to choose components that will make his product sound best.
