As I understand the BSW speaker system, you are now tied to the factory amplifier. Their system does not have crossovers, it relies on the crossovers in the factory amp. At this point I would recommend installing the Integral Audio subwoofer and amp that you already have and then re-evaluate at that point.
Don't get hung up on the number of speakers; what you're really interested in is the number of channels. The 5.25" speaker in the kick panel, plus the mid-range and the tweeter in the door all combine to make ONE channel. The other side front 3 speakers make up ONE channel.
Each rear speaker is ONE channel. The sub can be ONE or TWO channels, depending on your car's configuration.
'01 BMW 330Ci
'04 Volvo C70
'87 VW Cabriolet