I built one off of a Savage. Let me give you some advice. I know others will poo poo it, but we found it's a solid rig. My cousin built a 338 Lapua Mag on the Target action Savage. It is a SINGLE feed only. It will eject a fired casing, but you will have to pull the bolt to get a loaded round out. IF... you are wanting a long range rig, single feeding is not that big of an issue. The reason I make this advise is due the the trigger being able to be adjusted lighter (6oz-1.5#), and the action is very sturdy (more material due to ejection port design and no magazine).
My cousins rifle has a 32" Douglas with a taper to .900" It is a small shank, but due to the length the gunsmith that put his barrel on, put it on like any other action. The 28 and 30 will work fine with a barrel nut. If you want it to be a repeater, then you will definitely have to go with the a normal long action. They only make one action longer and that is for the new Lapua mag models they have. As far as I know, they are not selling the Lapua actions as a singular action.
Another option would be to get the Stevens 200 LA and build off of that. It will be a little cheaper. You can buy any aftermarket Savage trigger assembly and install it on the Stevens. The problem you are going to run into with any LA is using VLD style bullets due to their length and seating depth. If you get lucky and find a deeper seating depth of .050-.120" for accuracy any long action should work. But most like to be seated .010-.020" off the lands. So single feeding an action could be a reality w/o going to a custom action built for longer rounds with longer bullets. I could be wrong. I know guys are building them in repeaters.
I like Lothar Walther barrels. They use a harder Stainless Steel (550SS) than here in the states (416SS). It took a little longer to break in, but right now I am holding .25MOA to 800yds with a .308 Win. I have around 800 rounds through this barrel right now. A 1:9 would be good if you want to shoot the 240's, but with Berger's new 230 and 215 grain bullet, the 240 is really not needed. With the speed you can push the 208 A-max and 210 Berger with a RUM, a 1:10 would be perfect. 1:10 will also be able to handle the 215 and 230. You never know, your barrel may handle the 240's also due to the speed.
I suggest going with one of the money saver stocks from Stockade stocks. He has many different styles that will work with you rifle. They don't require a whole lot of finishing work when you get them. I was rather impressed with my cousins. I am kicking myself for not getting one when I had the chance.
You'll want a different recoil lug. Get an SSS pinned recoil lug from brownell's. They are sturdier and thicker than the stamped one that comes with the rifle. EGW 20MOA base is very economical and a good base. I like mine a lot. You might want to look at Burris XTR rings. I have the Weaver Tactical, but not sure how they would handle the heavier magnums. The XTR's will do great.
Tank