Don't do it.
This is not a conversion that's wise to do even on a standard LA magnum receiver.
Savage (and Remington, others) use different actions for the .338 LM which are designed to handle the very high bolt thrust generated by this cartridge. No doubt, there will be those that will say they've done it, or know someone who has...it's your head behind the bolt. The manufacturer says it's an unsafe conversion.

In fact had a conversation with Jim at NSS about a year ago, customer wanted a custom .338 LM and this is what I was told...and Savage does not allow their .338 LM actions to be sold by Dealers, either so they're non-obtainuim unless you buy a used rifle.