ok, my 2 cents, the 12 ga. with a slug that you can shoot accurately to a 100 yards will work just fine, to kill an elk, mule deer or any like game animals,
BUT the question is, can you shoot it well at a 100 yards with a bead front sight?, odds are the honest answer is NO< as its not a very accurate sight system, for slugs
NOW< if you wish to hunting with slugs I would strongly suggest BUYING a true slug barrel for your 870 that has good adjustable sights, it will allow you to be much more accurate consistently!
and then there is the issue about distance of shots and drop of slugs, with today's modern slugs and good barrels and a good scope that has preset reticles for drop of slugs, , again a good slug gun IMO can be just fine to use on the desired animals, but your going to be limited on distance of maybe a 150 yards and less, and I would maybe suggest staying under a 125 , for elk!
and this sounds bad to many rifle hunters that love the long range options, but to be honest many many MANY elk, deer and even pronghorns are shot by bow hunters and muzzleloaders at much closer ranges and even rifle hunters, every yr, and will even say a large percentage are at under a 150 yrds with many rifle hunters too!
YES a slug gun will decrease your shooting distance options, but it can be done if one wants too
so honestly if you want to use a 12 ga, it can be done, but it sure wouldn;t be my choice of a hunting weapon if I was spending a LOT of money traveling far to go on a hunting I dreamed about or worked hard for, as there are just many more rifles today in lower price range that can offer you higher percentage odds of filling your tags out west in the wide open spaces many of these animals live in, but its not a must have, if you set uop your 870 correctly and can shoot it well!
But again, the costs to set up your 870, odds are you can BUY a new rifle and then have an added weapon to your inventory of things, rather than just having a older shotgun with new parts added to it?
which would need removing if you wished to use in for small game or targets like clay birds and such.
but again your call! it can be done
I have been out west countless times and been well under 50 yards away from all 3 species your considering, so know the distance can be done! if your hunting skills are up to the task!