Here is a quick look at what a 30-06 with an 18" barrel can do with the 212 gr Hornady ELD-X. There is also a 220 gr ELD-X but has a slightly lower BC and the OP is interested in occasional shots out to 600 yards.
First, 212-220 gr expanding bullets are good bear medicine, especially in the hands of a shooter who is comfortable with the rifle. The shorter barrel means easier maneuverability in the tight areas where fractions of seconds may count.
Second, even with a muzzle velocity of about 2530 fps, the bullet drifts only about 27 inches in a 10 mph wind at 600 yards. Going to a 300 RUM drops that by just a few inches.
Third, one can zero at 200 yards and the bullet will be within 3 inches of line of sight out to 240 yards, which is adequate for closer shots where time is critical. There is plenty of time to lase at the longer ranges and make adjustments to one's sight or hold at the longer ranges. Goinbg to the 300 RUM adds only 30 yards to the maximum point blank range.
Fourth, a brake will help felt recoil
Last, there are commercial reduced recoil loads for 125 gr loads and tons of load data for the weight class with muzzle velocities of 2800 fps and lower. Those bullets are good for all North American deer sized animals.
Bottom line, the 100+ year old "ought six" is still one of the best choices for a "do-all" cartridge.