If it's a Savage made cocking piece, my guess is that it was what was in the bin when it was assembled at the factory. All the early Mk.1 and many Mk.1* rifles had the Mk.1 cocking piece installed at the factory until supplies were exhausted.
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It would have had a Mk.2 300-600 flip sight as original from the factory. The pressed steel Mk.III would definitely be a later replacement.
There's nothing wrong with two groove barrels. Some of the best shooting No.4's I've had over the years from both North American and Britishproduction were equipped with them.