A little clarity needed here.

Quote: "My issue is that the Savage extracts the fired brass just fine, but fails to reliably eject the shell, even when operating the bolt quickly and forcefully. The empty brass often just ends up sitting on top of the magazine, or between the magazine and receiver wall. Loaded rounds eject just fine. The brass in question is brand new Winchester cases." End Quote

So does it not eject fired brass, or does it? Does it eject your older brass, but not the new Winchester??

If your problem is JUST the new brass, my guess is that it needs sized/trimmed.
Just because it is "new" brass doesn't mean it is sized, or trimmed properly. Did you run it through a full length die FIRST, then check trim length??
If you can eject the older stuff and the new stuff isn't flattening primers, then it sounds like the brass is sticking.