I feel like I have to play the SHL5s loud to make them come alive. I’m very sensitive to upper frequencies going too harsh/bright.
As what Arafiq mentioned. Older SHL5 is slightly spitty and harsh in the treble in comparison to SHL5 Plus. It may be worthwhile to try the SHL5+ without losing the smooth and warm midrange of the Harbeth. The Plus version sounds smoother at the top without the glare and grain in the treble, and the bass is hugely improved and slimmed down with improved definition and detail.
The Graham equivalent is another good alternative to the Harbeth with a rather similar sound signature but with slightly more open, expressive and nuanced delivery.
With human voice reproduction, there are not many modern speakers that can match British BBC speakers, in my limited experience.