Your Browning is not a traditional Winchester design Highwall

The extraction system is different using a moving spring loaded extractor.

Winchester Highwalls have a manual extractor that sits behind the rim and levers out the cartridge.

http://www.wyomingarmory.com/gun-parts.html

I had one of these in 300 H&H that never worked. I converted it to 300 H&H Flanged (rimmed) and it worked better but still was hard to extract a high pressure cartridge.

That's why the Browning (and the Ruger) have springs.

I have never seen a 100% original Winchester Highwall chambered for a rimless cartridge.

Paranoia strikes deep
Into your life it will creep
It starts when you're always afraid
Step out of line, the man come and take you away