Again, I have no stake in this project at all, but the Sako magazine will not accomodate 340 Wby factory ammo. Been there and done that, twice! Just grab a box and try it! Having said that, you can handload to whatever length you want, so there would be no problem that way. The problem will come when you try to sell it and have to explain to the purchaser that he can't use factory ammo, w.o. cutting the tips off or seating the bullets deeper.
I sold this exact rifle two years ago, and it was not a problem becuase the guy was a handloader. Of course, this is the case when you try to sell any wildcat.
Same goes for the 358 STA and the 375 Imp, just load to the correct length for the magzine. Rembo has a very fine Clymer 375 Wby reamer that he barrelled up a Model 700 with, but the 700 magazines are significantly longer than Sakos. You could, however, just seat the bullets to accomodate the magazine.
The 35-300 Win will get 225 gr bullets above 3000 with ease and neck tension has never been a problem. It gets 250 gr bullets there w.o. leaning on it too hard at all. This is not theory, but actual chronographed velocities from 24" barrel.
Here's a picture of the 35-300 Win loaded with a 250 Hornady spitzer and a 300 Win with a 180 gr SST for comparison. OAL of the 35-300 is 3.450 and easily fits the Sako mag.
The 375-300 Win will give 270 gr bullets over 3000, as well. There are two guys here in Whitehorse that I know who have them. Bob Nantel has the reamer for that one if you are interested.
Ted