This may be of interest, it’s a What HiFi review that discusses the speakers various merits.
All I would advise is you “actually” compare the sound via your current Dac/Amps going into the Kii’s versus direct from Mini going via Contoller into Kii’s, and at £12.5K I would expect/demand that any dealer does a HOME demo.
But I would draw your attention to the reviewers conclusion in that they are technically brilliant but not quite at the level you could love, which to me means they miss that special something that makes you want to continue listening (something again you really need to check via auditioning).
The other consideration is £12.5k on Kii (ie. Amp/Dac/Speakers) and £450 on Streamer (Mini) could be viewed as a little unbalanced, again we know that the Mini punches above it’s weight but you may need something a little better on the front end to release the Kii’s potential.
Lastly the Kii’s appear to be a beefy speaker that can go very loud, do you have the space/room for them to work correctly, we all appreciate having small speakers in a large room just doesn’t cut it, equally too much speaker in a small environment can be just as bad!
Really can’t comment on there sound personally but from various online reviews they do appear very good, but remember speakers more than anything else are very “personal” and “room dependent”, although the Kii’s should make that less troublesome due to there adjustability.
Hope some of the above helps and happily listening.
PS. This review by Jason Kennedy has no such doubt (ie. no missing love factor), just goes to show how differently things can be perceived.