The Remington pump action rifle has one major advantage over all other types. The pump action rifle is the only manually operated action which allows the shooter to cycle the rifle without breaking his firing grip. Should a followup shot be required, it can be made faster with the pump, than it can be made than with any other manual action. My experience with the Remington pump is that they tend to be more accurate out of the box than any similarly chambered bolt gun in the same price range, not that mechanical accuracy is a major consideration in this application. If the comparison was made between the pump and the semi-auto against multiple targets, it would be a mistake to assume the semi-auto would engage each target faster, the difference in speed lies more with the individual shooter. The Remington pump has a nice flat profile, it balances well, and additional magazines can be loaded and carried in your pockets or in a pack.
If the pump action proved to be the rifle of choice, I would advise that some small changes are made to the basic rifle. The first consideration should be the butt stock. The M-7600 rifles of recent manufacture seem to be adorned with an unfortunate Monte Carlo profiled stock which has such a high comb that shooting with irons would be impractical unless they were somehow mounted very high above the bore. In wood , the comb can be reconfigured, but the plastic one is a problem and should probably be replaced with something more suitable. The older classic style wood stock has the correct profile and comb height for shooting with iron sights, and its easier to correct the length of pull of a wood stock than a plastic stock. That is the stock that should be on this rifle. The open sights should be changed to a ghost ring and post, which are both faster and provide greater precision than an open rear sight with a bead front. The rifle should have a simple 1" or 1.25" sling attached to it.
My person prejudice lies with a bolt gun, but only certain bolt guns. There are many other viable options provided you stay within the parameters of a major caliber, in an iron-sighted, light weight, short, repeating rifle. Should the lever action be more to you liking, the BLR is chambered for modern cartridges, but the M-71 and 1886 Winchesters, although expensive and difficult to find, are chambered for all sorts of big bullet bear killing cartridges, as is the 95 Marlin chambered for .45/70. Both the Browning BAR and the Benelli R-1 can be had in .338 Winchester, if you prefer a semi-auto, and the gas action does mitigate recoil somewhat, but these rifles tend to be expensive, and some folks balk at the idea of an expensive rifle being exposed to the elements of a long wilderness adventure.