From what I've read here it seems that the 338 Lapua is not recommended for the standard 110 series action. Hopefully some more experienced folks will join in here but my understanding is that your best options are build off a different action, find (good luck, as you said) a 338 action, or go with a 338 Edge or similar. As you are already set up to shoot the Lapua I can see how and Edge or Rum wouldn't have a lot of appeal.
Again, hopefully others chime in and can help more. In any case welcome to the board and good luck.
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