BT3s are a rather nice, plug and play setup but I can't really see how they would improve on your current setup.
Your dismissal of active monitors does leave you rather at a loss, the vfm of, say, the Yamaha HS5 at less than £250 is simply not matched by any hi-fi type speakers that I know of, genuine active systems from 'hi-fi' companies are far more expensive.
You could look at the Audio Engine A5+, another powered design, which gives more of a 'hi-fi' sound, but they are pretty big for the desktop, so I guess you are left looking at one of the small Denon or Pioneer amps from Richers with, say, a pair of Dali Zensor 1, though again, this is more of a sideways move than any great improvement.
If you don't need the facilities of the DA300, you could sell that too and look at the Kef X300 (£600) but that would be a shame as I am guessing that is quite new and rather good.
So.....*unknw*