You have a splendid rifle. And you are correct that Smith-Corona made most of the parts. Barrels were made by High Standard and Stocks and Handguards were also made by a subcontractor.
Remington was indeed authorized to transfer some early parts to Smith-Corona. I know that stocks were transferred. And I have seen a few other small parts to include front sights. But I believe some of the Remington parts on your rifle may be replacements made by a previous owner.
Thanks again for sharing!
J.B.