I just keyed in Stiller rifle actions, and it went right to their home page. The Lapua is an excellent choice...a little less powerful than the Remington RUM, but not enough to make any difference. I have both, and I like them equally well. My 338 Rum is, as I posted before, just a Sendero that has been rebarreled because they do not make the Sendero in .338, just the .300. I enjoy high end rifles as much as the next guy, or I would not have spent $9000 on my Lazzeroni, which is what it cost by the time I paid shipping, tax, and put a decent scope on it. But if you can get what you want for a lot less money, sometimes you have to admit that your ego is driving your wallet. (I did not mean to call you egotistical, but I see that happening all the time at the range.) I have a Sendero that my wife bought me for my 50th birthday 16 years ago, and it will still put three bullets in the same hole at 200 yards, and I have the targets and witnesses to prove it. This is an over-the-counter gun that has never had any work done to it. My .338 RUM puts three in the same hole at a 100 yards, but I have not shot it past that, so I cannot make any judgements on its long range capabilities. My Lapua is a CZ 550, but I have not shot it much yet, so I can't say much about it except that it is not a hunting gun unless you are a serious masochist who likes to crawl the last mile back to camp. It weighs over 16 pounds without the scope or sling. Savage and Remington both make excellent rifles. I do not own a Savage, but John Lazzeroni would not have agreed to license them to produce at least one of his calibers if they were not high end rifles. The problem with building guns by buying one part here, another part there, a third part somewhere else, etc., etc., is that sometimes you get a pile of excellent parts that don't add up to a good gun. A good smith can always make it all work, but the question is, is it the best you can get for the money. That is why I bought the Lazz. Let him do all the experimentation and then sell the best rifle on the planet. I would give my left leg to have one of his tactical .338's, but I already gave my right leg to get the Warbird. All I can say is that you need to do a tremendous amount of homework before you start buying parts. Are Stiller good actions...of course. Do they work well in Macmillan stocks...who knows? Those are all the little details you have to work out before you even start buying parts. All you need to ruin the whole project is to have part F not work well with parts ABCD and E. But, on the other end of that spectrum is the fact that you can go to the range knowing that you have a really special rifle that NO ONE else has, and that feels pretty neat. If you plan to AI this rifle, take that into account when you order your barrel. You need to keep your bullet rpm's under 295,000. Also, when we are talking about high performance rifles, you need to keep the barrel squeaky clean, and while shooting, do not let your barrel get above 165 degrees. Do those three things religiously, and your barrel will last forever. Since you are on a budget that will pretty much get eaten up on the rifle, you will have do something about a scope. There are lots of expensive optics, but you can get a good variable scope for under a $1000. I have a bunch of Leupolds, and I don't really like any of them. Zeiss makes a nice scope, but I have had trouble getting warranty work done. Whatever the problem is, the warranty never seems to cover it. Plus, I sent one in for some work, and it had mil dots when it left, and they were gone when it returned. They would not admit that they took the mil dots out, so I was screwed on that one. My latest scope purchase is a Vortex Viper PST, 6-24, 50 mm objective, 30mm tube, and it is a great scope. Warranty wise, I have read (maybe on this site) posts from two guys who sent in their scopes for work, and the Vortex people just sent them a new scope, no charge. Hard to beat that. And, the warranty is lifetime and transfers with the gun. Cabelas sells them for $900. That is probably way more advice than you wanted, but good luck on your project. Be sure to post the outcome.
On the part about the RUM beating the lapua Long Time Long Ranger has stated that the Lapua will slightly beat the the RUM due to the higher quality Lapua brass being able to withstand higher pressure. http://www.longrangehunting.com/forums/f17/338-lapua-mag-338-rum-63472/
As to who knows about Stiller actions working well with McMillan stocks.....there are lots of Stillers sitting in McMillans that work very well. Len even sells McMillans inletted for Stiller actions right here in the LongRangeHunting store!
Keeping the bullet rpm below 295,000 will be easy to accomplish as long as my math is correct. A 300gr Berger shot at 3000fps in a 10 twist barrel will only be spinning 216,000 rpm. MVx720/10