I was told friday by a reputable gunsmith that a 300 win mag is a more effficient cartridge than the 300 ultra mag. He also stated that you couldn't possibly shoot accurate with remington ultra mag brass because it is "junk". I on the other hand have not seen a ultra mag yet that wasn't a stone cold killer and accurate to boot. I really don't care if it takes 93.5 grs. of retumbo to move a 220 smk 3150 compared to 77 grs. to move the same bullet 3000 fps, as long as it KILLS EVERY BIG BULL I POINT IT AT! You might want to do a little research about some of these subjects with somebody with more knowledge than me. Did you also know that a 338 lapua is accurate because it "looks like" a 6 PPC case, interesting huh!!
What is the rate of twist in your current barrel? The primary reason for choosing a 300 RUM over a 300 Win Mag would be to push the heavier bullets faster. If your current Stevens barrel cannot stabilize the heavier 210 - 240 grain bullets (requires a one in ten twist), then it may not make sense to incur the cost of the rebarrel; opening of the bolt face; and complete magazine change out on your Stevens. Just something else to consider.
Ballistically, your 300 Win Mag should be good out to 1000 yds. I would stay with the 300 Win Mag and practice until the barrel was shot out before making the change.