I had an LS5II for 6 years then sold it which was dumb so I turned right around and got another. Then I sold that for a MK III for just a couple hundred $$ more. The MK III is much more refined than the II...particularly with a more natural top end. It was finally the BAT VK31SE that was a significant step up from the LS5.
I started with a 30SE but it was lifeless on the top and yet far more resolving and a more natural 3D presentation than the LS5. But then I upgraded to the 31SE and WOW....what a magnificent product! The super beefy dual power supplies in the BAT bring on a bass rhythm that was lacking in the LS5. After owning the BAT now for several months, it would be very difficult to return to the LS5 and that is itself one heck of a product. Pure and simple the BAT calls far less attention to itself as a piece of audio gear. So go try one of these out.
The LS16 is not at all in the same league as these. And I did hear the LS25II and it was quite nice but it too was too forward compared to the at-ease presentation of the BAT.
I can swap cables and amps and eve speakers and happily live with many combinations. But I too have become incredibly finicky about what preamp locks in the magic of my system. It does seem to make the biggest difference to me as well.