I have found asap to be a bad way to build a rifle. I use shilen barrels on everything. I have had wonderful consistent results. I was impatient for a 6.5 wsm and called around and mcgowen had the fastest turn around, I wish I would have waited. There is nothing wrong with the barrel it just isn't up to the standards I'm use to. I would check northlander and see if he has any in stock, I've never bought from him but I know he keeps certain chambered barrels on hand.
I would go sporter if you are going to be carrying it and hunting with it. If you are going to be a lot of target then go varmint contour. Only you can decide that. You can wrap sandpaper around a dowel rod and sand the barrel channel until it is right just make sure you keep the channel straight. If you are going to bed the tupperware stock I recommend stiffening the forearm. I did one with fiberglass and aluminum rods and it came out great.