Phase and time alignment are two separate issues. A sub can be in phase with the main speakers but two cycles late. The sub has to be in phase and on time. The only ways to adjust time are either by digitally delaying the "late" speaker or moving the speakers relative to each other. That can be 15 feet or more in some instances.
Good, you are a serious listener. I hate to waste a lot of hot air on someone who is not.
The low pass filter that most subwoofers have is only good for mediocre performance at best. The same holds true for subwoofers that have passive radiators. Rel makes subwoofers that can be added to a system in the least expensive way possible.
Part of the beauty of subwoofers is that they allow you to remove distortion creating bass from the main speakers. The result, besides cleaner sound, is better imaging. This requires a two way crossover that puts a high pass filter on your Focals. Unfortunately, you have traveled down a road with a dead end by getting an integrated amplifier that does not have an amplifier input. You can not use a crossover or processor with it. If you wanted to do this in economically acceptable steps. You need to get a stand alone amplifier. Hegel makes several of them. Your dealer may allow you to trade your integrated in. Along with the amp buy a MiniDSP SHD digital preamplifier. They are only $1300. The SHD will measure your system with a microphone, correct many problems and provide a full crossover for your subwoofers. Next and last would be to upgrade the subwoofers. Two 12 inch units by JL Audio or SVS will do. If you think cables make a difference, wait till you get a load of this!
If you decide to go this way and have any problems setting it up feel free to message me.
Mike