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You would not want a rimmed case if this was going to be done in the BLR, as it would be a nightmare getting it to stack and feed properly in the detachable magazine. It might be able to be done in a Model 71, but would surely be a challenge.
I know for certain that at least on BLR has been rebarrelled to 358 Norma Magnum, and worked! Started out with a BLR in 7mm mag and went from there.
Certainly a 416-300 WSM job could be done, however my guess is that it might be a bit of a challenge getting those fat cases to work properly in the BLR magazine.
Why not just do one up in 416 Taylor? It is the 338 Win Mag necked up to 416, and wouldn't be a lot more difficult than the 358 Norma project.
but if you started with a newer Browning BLR chambered for a WSM short mag perhaps the feeding problems would be not too difficult to overcome. Barrel contour may(?) need to be larger and fore stock modified to suit - AKA the BLR 450 Marlin barrel profile and fore stock.
Noveske has been necking up the WSMs for a while now. He lists the 416WSM as an optional chambering for his custom bolt guns - http://www.noveskerifleworks.com/chambers/