Pharsyd, welcome to the Circles!
From what you describe, I would say yes, you take the sub out from the EAD, connect it to the amp for the passive sub, and then the sub from that amp - the EAD should then feed the sub amp, just sub signal.
As for building your own passive sub, I have had great success with buying drivers, and building boxes. In Ontario there are some places to hunt (in Toronto there is Audio Hardware Inc, The Speaker Shop). I had pleasing results with buying a 300w Class D amp, and then building 2 subs. One is a ported 12 (4 cubic feet, tuned to 23Hz for movies), the other a sealed 12 (1.5 cubic feet, for music). I just swap the speaker cables to change the bass monster, for whatever genre I am looking for.
Mark in Burlington