I would go 300WSM and start out trying the new 168 grain E-tip. It could easily be lauched at 3100 FPS and is still travelling at 2050+ FPS and carrys over 1550 ft/lbs KE at your max range of 600 yards. That assumes 1,000 ft elevation and most elk hunts
are 5,000 ft or higher so your downrange numbers will probably be better.
The min impact velocity is 1800 fps so you would still be over 250 fps above that value and the bullet would surely penetrate with 95% weight retention.(Probably better than the 180s) It has a .503 BC which runs right with most of the 180 grain premium hunting bullets also.
Kimber Montana would fit the bill for a lightweight carrying rifle and the savage weather warrior are right in there also.