I shoot a 300 RUM so am a little partial. I do think it would give you a little advantage over the others mentioned because of the high velocity and potential for high b.c. bullets. Takes some of the guesswork out and packs plenty of whallop at a distance. If your rifle will shoot them, you might try some 210 bergers. I shoot my own bullets with very high b.c and have dropped several elk at 1000 yds.......Rich
IMO, the 308 is not near enough rifle for a 1000 yd shot on a mullie... unless you just want to punch a pencil hole in its side. I also belive the 300 WM comes a little short of a good 1K deer killer, as does the 338 WM, 300 WSM, 7RM, 7WSM, etc., simply because none of these will deliver a bullet 1K down range with the velocity required for expansion. There may be 1 or 2 bullets you could use that expand at lower velocities like the A-Max.
By far the best cartridge on your list is the 300 RUM. It will get you a little beyond 1K with most expanding hunting bullets with a good BC.
At sea level, I would feel safe about the 210vld expanding up to right at 900 meters as max range for elk hunting(still retain 1700fps).
900 Meter = 984 yards.
8000ft above sea level is a whole new level, Max range would be just under 1200 meters (1700fps mark).
Pesky ol' air density effects...
A 300 RUM should easily be able to push a 210 VLD @ 3100-3150 fps. The Berger VLDs are advertised to expand down to 1800 fps. @ 3000 ft elev, the 210 out of a 300 RUM should be a 1K plus cartridge, almost to 1100 yds.