I love the looks of full stocked rifles. Tried to get my friend with the Ruger International to sell me his but no luck. (A poor friend he is, one who won't let a good buddy beat him outta such a nice rifle!) It only shoots middling accuracy, maybe 2" consistantly, but it handles great. For the use that rifle is best suited I wouldn't even change its mediocre trigger. Shoot it with irons or a compact, low power scope for a fast handling deep woods deer rifle.
Full stocked hunting rifles usually have light, short barrels. The extra wood improves balance and provides a small measure of protection for the thin tubes. Seldom do they have tack-driving accuracy but it's a hunting rifle, not meant for target shooting. They are best suited to short range hunting, less than 200 yds. Hunting mostly in deep woods target accuracy wouldn't even be an advantage. But good balance in a small package is a BIG advantage!
Any medium capacity, large bore (for its capacity) cartridge works fine in short barrels. Large capacity cases and smaller bores don't do so well. The "powder expansion ratio" of the .308 allows it to attain almost as much velocity in a short barrel as a long one. Thus, your choice wouldn't be as good in .243 or .260, while the 7-08 would be almost as good and the .358 would be even better.
Your ideas are sound and your choice of a .308 RSI is very good. It will be a great rifle IF you use it in the right way and for the right game!