It's going to be a bit of a challenge to find speakers significantly "better" than your current ones (which are very good), especially at the 6K point, even factoring in used.
I second the advice of starting to explore what's out there. Bear in mind, too, that at stores or shows the whole system is new to you, not just the model of speaker you're listening to.
Beyond standmount+subs versus floorstanders, consider, too, that Harbeth 40.3's, Spendor Classic 100's, Graham LS 5/5's, etc., are all technically standmounts.
I second the advice of starting to explore what's out there. Bear in mind, too, that at stores or shows the whole system is new to you, not just the model of speaker you're listening to.
Beyond standmount+subs versus floorstanders, consider, too, that Harbeth 40.3's, Spendor Classic 100's, Graham LS 5/5's, etc., are all technically standmounts.