The Hawkeye and the Alaskan are 2 models of the Ruger rifle. Sorry.Reboring a .375 Ruger Barrel to .416 Ruger barrel would be like scrapping a Spitfire to make a Mustang!
There should be many .416 barrels to find on the shelf/with manufacturers. Buy a .416 barrel off the shelf vs. waiting 6 months to a year for a .375 to go through a boutique shop's work queue to get it re-bored. Then your riflesmith cuts the .416 Ruger chamber vs. .416 Rem/Hoffman/Taylor, as an example.
Don't understand "Ruger Alaskan? Hawkeye?"
Yes a 416 Taylor great option, only down side is no factory ammo ,very easy to form brass out of 338 or 458 & that's readily available. get an action or rifle in 338 WIN & your ready to go, no mag feeding problems or bolt face mods i did one from a old mk1 Ruger African 458 worked a treat. A HOWA 1500 wood stock 338 would be a good start.And the 416 Ruger takes someone with real experience to get to feed on a conversion. A 416 Taylor would be easier on a magnum-based action.