So the one thing you know for sure is the Bryston amps sound tinny and bright, but the one thing you want to try is new speakers? Just want to make sure I understand the question.I also can see what people mean about Bryston gear sounding a little tinny or bright at times.
If I were to evolve the system, would speakers be high on the list, and recommendations given this hardware?
The One Rule that has served me well over 50 years is always work on upgrading the weakest link. Your One Job is to find the weakest link. Could be anything from power cords to speaker cables to the cones under the components to the lowly fuses inside them. Yes even the room is fair game. Anything and everything.
Now out of all those things you could be looking to upgrade, there is one and only one component you take the time to tell us you know is flawed, and another one you take the time to tell us you don't think is flawed. So which one is it again you think you should be upgrading?
While you're mulling that one over, here's a freebie you can try that will probably help a lot.
Swap connections to run the B&W direct and full range. Do not use the sub crossover, except to adjust the sub. Right now you have your mains being driven by a signal you're sending through two extra God knows what interconnects, the assuredly crap crossover network in the subs, and then back to drive your speakers. Every one of those steps involves wires and circuits each one of which is adding a veil of grain and glare, which is also the problem with the Brystons. So you've unwittingly made a bad situation worse.
Running the B&W full range will also improve bass response, probably by quite a bit, because the more bass drivers the better.
But hey, don't take my word for it. Try it and see. Go and listen.