These are not extremely high pressure racing springs. There is no need to remove the inner spring. As I said before, Lunati does have some experience in this field so let's not confuse the type of cams/springs that the magazines discuss with street cams.
Personally, I prefer running a commercially packaged break in oil since they are available these days but using the additive works very well today as it has for the last 50 years. Personally, the main reason that I don't like using synthetic oil during break in is that it's going to get drained and replaced shortly after break in and it's a lot of money down the drain.
In the end, take the cam manufacturers suggestions and follow them in this field.