I've actually got both of my #1s now over with another gunsmith working on them.
He's got my daughter's .308 RSI International, putting a laminate RSI International stock on it. I had to get the laminate mannlicher stock made custom. In addition thereto, I'm getting my 1H .375HH converted to an "RSI-esque" mannlicher stock on it also, and the same fella who made the laminate mannlicher stock for my daughter's .308 is making an identical matching stock for the .375, but widened and inletted around that heavy barrel.
I'm still going with a 20" standard mannlicher fore-end on the factory 24" .375 barrel, so the overall profile when he's done will be something akin to a falling-block single-sock Nylon 66 look, with the stubby barrel sticking out the end. Or like the really old-school Mausers for those familiar with them. I was concerned about the barrel-band forward of the standard fore-end, but the smith told me not to worry, he had a way around that - so I'm looking forward to seeing them when he's done too.
My thought behind it is to get a pair of matching, go-anywhere, do-anything #1s in stainless laminate, and have them as "father/daughter" rifles my daughter and I can go out together as she grows. Of course, in another 10 years or so, I might be wanting her to take the .375 and I'll shoot the .308

I don't have any pictures yet of those getting worked on, but once I get some pictures, I'll share them out.