You need to visit a dealer and do some listening. The limitations you list in regard to your KEF speakers sound like common characteristics of Arcam amplification to me, so it would be sensible to investigate amp and/or speakers within your substantial budget. It's quite possible the right integrated amplifier, combined with the right speakers, could bring you a more worthwhile upgrade than exposing deficiencies in the amplification.
In your shoes I'd be looking at Rega, Naim and Hegel amplification, but then they are my favoured makes of amp and may not be yours, so we're back to auditioning. Same with speakers; I'd be looking at Amphion, but you need to do some listening - first in the dealer's dem room, and then at home, before you take the jump.