Another thought, at the other end of the frequency scale, treble, the Tannoys are merciless in revealing roughness in the top end. A lot of class D amps are optimised for 4 Ohm speakers, that is a flat frequency response in to a 4 Ohm load. If used with a higher impedance load, top end treble is likely to be emphasised.
In this case the output filter capacitors should be changed. I sometimes run a Class D TPA3116, it's pretty good, but this treble emphasis can be heard. I should really change the filter capacitors as mentioned.
I generally run Rogers BBC LS3/6, which have a tapped auto transformer on their input. This would allow me to change the input impedance to something lower and around 4 Ohms if I wanted. I have not tried this as yet. My favourite amp with these speakers in a Radford STA25 III.