I had a 300 wm heavyweight bullet setup for a few years, and enjoyed it. It was before the 300PRC, 30 Nosler, etc. I did for fun, and I learned a lot. I still have the rifle, it is a plain jane Browning A-bolt with BOSS that i bought off my cousin. One of my dad's iron worker buddies who had a lathe in his garage and a reloading press setup in the living room talked me into it and helped me. I watched that guy reload stuff all the time with a Marlboro hanging off his lower lip. He's still at it today, but uses nicotine gum. Cigarettes are too expensive i guess.
I think my OAL was somewhere around 3.620 or so. I ended up just single loading it because the Brownings are almost impossible to run with over-length cartridges. Wasn't near as bad as I thought it was going to be loading one at a time, at least the browning has an easy to reach bolt release so unloading a live round was easy enough.
I decided to throat out my rifle just a bit to get a some jump in it to run the longer bullets seated out in the case neck without stuffing them way down deep into the case. That's the only way I'd do it, seating them way out. Otherwise I would suggest some of the newer cartridges because the WM just doesn't quite keep up with the pace if you stuff them deep. I know, we tried.
I shot 200 grain bullets mostly, and felt I was slightly limited by twist rate but i didnt have the bullets we have now. I had plenty of success with it out to 1k, about as far as I cared to shoot. Mostly shot at rocks the size of a hay bale at that range. Killed and elk super easy at about 800 just like it actually wanted to get in the truck for us. I never really worked up much ballistics with it, used a fair bit of Kentucky windage because the scope I had didn't give me enough elevation past 800. Didn't have a chronograph back then either, we used the charts in the back of the Nosler manual and guesstimated. Then I'd get lucky and hit a small rock with it and always would want to go back to the same holdover. Young and dumb I guess.
To stretch it out further with that particular rifle, looking back I would have wanted a better scope with a 20 MOA rail setup, a little bit faster twist and a different bullet. That's another advantage to the newer cartridge/ammo offerings. I really liked the rifle even with the shorter lighter barrel because of the BOSS, so much that I still have it.
Since you're building from scratch, you can avoid the twist rate issue. You need to find an action/magazine you can load Looooonnngg if you want the Win Mag to really shine. Try to control the runout as much as you feasibly can. Especially if you're wanting to go up to stuff bigger than 212 or 225 gr. I'm not really sure you will make out as well as you expect with the 250 amax, but you will be the judge of your own success.
If i were to do another big daddy 300 WM for myself today, I would probably take a free head start and begin with a Christensen Mesa LR and just be done with all the action/mag length hassle. They are pretty long boxed. I've had a couple Christensens and never a complaint. Just my opinion.
I do have a friend that currently has a 300PRC and it is very nice, and it shoots 208gr Barnes bullets very well. Under 800 its a sledgehammer. That's as far as I have seen it shoot. One time we had to bail out quick and take a 575 yard shot without much prep time....piece of cake. Very impressive. But you are here to hear about the WM, so I will say that you will probably be very happy if you do it right. I could confidently say my old A bolt 300 wm would have done most things as easy as his does. Especially on this continent.