Hi Andy,
Yes, I have seen several of the 375/303 cases loaded with the copper-capped sporting bullets, all of which cases having various Kynoch headstamps. I have also seen Eley cases with soft-nosed bullets in. However, the only bullets I have seen in the KN and BM&MCo cases have been the pointed match bullets.
As a "new" calibre in 1905/6, I am sure rifle manufacturers would have chambered not only Match rifles, but also sporting rifles for this round, and Kynochs would have been keen to push ammunition sales therefore, and so would have loaded various styles of sporting bullets. As the calibre became more popular, Eley Bros would have taken the opportunity to produce their own ammunition (although I do not think they could have made very much, as their h/s in this calibre is quite scarce.
KN were better known as makers of accurate target and military ammunition than of sporting, but there is no doubt that they could have loaded this calibre with sporting pattern bullets, especially if they were asked to do so by a client, so there may well be such rounds out there to be found.
Hope this helps.
Regards,
Roger.