I have never shot that particular Savage model. It has been my experience with most Savage guns, especially the older ones, that they were "overbuilt" and as folks in this part of the world would say, they are very sturdy. I believe that gun has a 2.75" chamber and that the steel used in the barrel was a bit softer than that used in modern guns so you probably will not want to shoot any of the tungsten-based shot or steel shot through it.
It's always a tough decision for me to make about shooting older guns, especially those with sentimental value. I like the idea of hunting with one, the way my father, older brother or some other family member did. Then I think about the fact that the gun may have some inherent weaknesses that modern ammo will bring out. I usually balance that out by only shooting "low brass" 2.75" shells, after I've made sure everything is as it should be with the gun.
As you know, the Mossberg 835 has a much larger inside bore diameter than the average 12 gauge shotgun so it does not do well with 12 gauge rifled slugs or any of the sabots. Mossberg does not recommend shooting slugs through the regular shotgun barrel that comes with that gun. You can, as you mentioned, fit a designated slug barrel to your gun and use it for deer. If you can find one of those barrels, reasonably priced, it would certainly be an option.
I do like those guns a lot and some of the very best patterns that I've seen have come from properly choked 835s.
"If he's out of range, it just means that he has another day and so do you."