Generally speaking, how much extra metal does one need on a barrel in order to be able to machine it to Octagon (so that it then comes out to be the correct diameter).

I ordered one of those Montana Barrels in .338 win mag. It got here quick, and is a nice barrel. However, for a #3 contour it seems awfully heavy. Thought maybe it would be a good candiate for a long term project using an octagon barrel.

Seems like that is all this company does, might give them a phone call or email them...here's the link:
http://www.cncbarrelworks.com/pricing.htm

No extra steel is required. A cylindrical barrel of any diameter can be made into an octogon barrel. The real question should be " If I want an octogon barrel that is 'x' across the flats at the muzzle or to have flats of 'y' width, what diameter do I need to start with?" or " I have a barrel that is 'x' dia at the muzzle, what would I end up with across the flats?" From that point it is a simple geometry problem. Keep in mind that you need a minimum of .100" between the bore and the flats.

The formula is 1.08 times the width across the flats is what you need in a round blank OD. For example, a one inch octagon barrel started out life as a 1.080 inch round one. Plus fudge factor just to make sure the points clean up.