You are already on the right lines, viz. high sensitivity speakers and SET valve amps. (The 'First Watt' principle..)
I'm well known as a low level listener amongst our Wam South Coast group - visitors are always commenting that I should crank it up a bit for them.
My main system is active horns but they are ruled out, so I suggest you make a beeline for Lancaster from the West Midlands and snap up my Jantzen TQWT floorstanders that Toms Wait is moving on.
They are cracking speakers and I think they are the equal of the LVs that you have but usefully more efficient.
Also, @ £550 they are a bargain.
A sub isnt a bad idea too based on my experience and the opinion of associates. I advise a damping platform under the sub. As it is bass that travels (into the next room) if the sub is active, as most domestic ones are, then you can control the bass, or even switch it out depending on who is in the house/flat.