Nice sound clip !
Yes, back 10 years ago or so, King Sopranos (straight or otherwise) had a very bad rep online for poor intonation, their Saxellos aside. I had refurbished around a half dozen straights by that time and didn't find that to be the case, however.
I mean, comparatively speaking to a Conn or Buescher or Martin of similar era...the Kings always seemed to possess a similar intonational attribute to their contemporaries.
Nevertheless, up until around 2016 or so, the Kings fetched less on the market in either project or refurbished condition. However, I have noticed in the past 2-3 years that their market values have increased, and people have been bidding numbers on a project straight which parallel the amounts folks will pay for a project Conn, Boosh, Martin.
So it seems the more attention these have been getting, their values have been increasing...which suggests (although doesn't 'prove', necessarily) that others are not running into the reputed 'bad intonation' issues, perhaps.