while powering your subs off your main amp really isn't recommended for a variety of reasons, IF we try to work within that limitation, there are some possibilities.
the first thing is that the subwoofer system must be as efficient as possible to get the most spl with the least amount of power. so let's think big ported cabs.
second, there is the possibility of using dual voice coil drivers and wiring each coil with one channel of the amp. that will at least allow you to double up the power into each driver. ah, double power!
28 cubic feet is just great. it can be a simple slot port and tuned to 18hz. that is the sweet spot between extension and spl output.
three drivers will cost about $200 or so each delivered, iirc, so well within your budget.
stereo integrity dual 4 ohm drivers is what you want.
here is the system performance with 3 drivers, 100 watts off each channel to each coil on the subs, for a total of 600 watts.
120db at 20hz before room gain is sufficient to move some popcorn. :-)
the specific form factor can be worked out easily enough.