Speaking only personally; resulting analysis of your expanded words.
First predicate that such factory work would almost surely add astronomical proportions to value. Ensuing red flags, automatic. Assertions easy. Yet ‘proof of the pudding’ challenge… In garnering ‘the’ proof itself.

In place of hard evidence, here speaking in probabilities. As noted, seriously doubting the Win factory to do such conversion. Simply not their ‘thing’. Your suggestion of middleman role, while seeming more likely, also remaining objectively quite unlikely. The principal & significant question of why? The factory putting themselves in the middle of such transaction merely exposure to possible issues. Customer satisfaction, warranty, even in Jurassic liability era, some concern no doubt of bad publicity if some kind of defect related mishap or even unhappy customer beating drum. Many good reasons not to be involved, none in context of presumably undistinguished rifle/otherwise ordinary sale. IF a particularly famous personage as customer; at least some possibility. But still… Balancing interests… Not!

What I could easily see is Winchester simply delivering the gun to some custom shop on customer behalf. But such involvement not ‘sexy’ in terms of collector interest beyond the resulting product itself.
Without hard documentation, my belief you’re swimming upstream against powerful currents. That and the gauntlet; experienced collectors, “factory original variation” claims, already moving into “hard hat” area! 🙂
From appearance and now your own hands-on observations, concluding a quite nice rifle of itself. One to be justifiably proud!

Bottom line to distinguish between “facts” and “lore”. Banter value, interesting! Economic context, often worlds apart.
Great communicating. Sorry if seeming the pessimist dousing enthusiasm!
Just another…
My take.