Re: What action would you use.
All of the actions you mentioned are great actions so you can't go wrong with any of them. I personally like the Remington 700s. However, having said that, if I was truely "building" a rifle, I would seriously consider purchasing a custom 700 drop in replacement action. There are several good actions out there and some with relatively quick turn arounds when ordered. For instance, I recently ordered and received a Stiller Predator action for a custom 30 Hart rifle I am having built and the action was in stock and shipped out immediately from Stiller.
The reason I say you should consider the custom action avenue is that once I figured out the cost of the Remington action plus the added costs to true it up and accurize it, it was actually cheaper (or at least no more expensive) to just purchase the custom Stiller action which is already accurized and is in fact, a better action than an accurized Remington (so I'm told by several very reputable custom rifle builders).
I'm not pushing the Stiller per se, it's just the one I happened to choose based on cost and availability. There are lots of "as good" if not better actions out there.
I guess my feeling is that since you're going to the expense and effort to match it up to a custom barrel, you're obviously thinking in terms of better than "average" factory rifle accuracy potential. For essentially no additional cost, you can step up to an action that fully compliments your custom barrel.
Again, I own and am very satisfied with several accurized Rem 700 rifles. all of which will out-perfom my abilities. It's just my nature to try to get the best bang for the buck (no pun intended) and when I wanted my ultimate hunting rifle, I decided the custom action route gave me more rifle for the same cost.
I apologize if I've taken this thread off course, it's just that I recently went through the same dilemma and thought this might be helpful.
Good luck with your project