Use the 375 bbl on your Steyr project.
Chamber for the 375 N/E rimmed 2.5" case
It was a popular offering in the British built Steyr, Martini & Lee sporters.

You can make a short version of it for the simplicity of obtaining brass by necking up 303British brass.
Then it'll be a 375 N/E 2.25" case .

I still owe you picks of my Romanian Steyr sporter carbine. Haven't forgotten, just haven't dug it out yet.