I’m having my Win Model 70 Extreme Weather (30-06) rebarrelled to 9.3x62. I tested it with some 9.3x62mm cartridges before I purchased my barrel and it feeds them just dandy. Shouldn’t require any extra work other than chambering the barrel blank and getting it spun on.
Who or what lash-up will rebarrel your rifle? I'm having a tough time finding someone or some company to rebarrel a 308 Norma to a 338.