Yes, Bose product don't get much love here. They do have some solid products and those get recommended even here, but in general their "design philosophy" hardly overlaps with AH view on good performance.
Be that as it may, some people love Bose, but the thing is a lot of their equipment is interdependent for the result they aimed to achieve. In other words, the only thing worse than Bose is a system mixing some Bose products with others. And the compatibility issue is not only in the sound but in connections and set up too.
I've listened to a system that had Wharfedale for fronts and, like you, it had some satellites remaining from a Bose system. Even though turning off the satellites in this particular case meant loosing certain channels, the sound was much more pleasing using just the Wharfedales.
I agree with all other members wrote; integration would be hard and maybe even not attainable.
Since you said you can afford it, see if you could get a system that would replace the whole Bose part.