RE: rifle or shotgun
You don't need letters that big to make your point. Why would you spend 2 or 3 hundred on a weapon that is less capable and the shells cost more than twice as much for (sabot loads)?
Are you telling me a rifle like a .243, 270 or 30-06 will not kill a deer at 50 to 75 yards? It most certainly will and will more than likely do it more efficiently than a slug gun will. I would bet the majority of deer killed even in rifle only states are shot at 100 yards and in. Remember a slug gun in most cases is a gun that was meant for one purpose and converted to something else out of necessity. As well as the ammo, the modern sabot ammo are just pistol bullets put in a sabot to fit the larger bore of a shotgun. Nothing real high tech about it to be honest.
Modern inline muzzle loaders in my opinion still have the edge over slug guns, but are still not up to par with a high powered rifle in terminal performance.
Can you use a shotgun at 50 -75 yards, sure you can if it shoots well enough. Plenty of people do it every year, me included. That doesn't mean you should limit yourself to it if you don't have to. I mean if you want to for the challenge feel free, but you certainly shouldn't feel like you have to if better options are available.
A shotgun is considered a close range weapon because that is it's LIMITATION, not because it excels at it.
You are never going to convince anyone that has experience with various weapons that a slug gun, or shotgun with buckshot is more effective than a high powered rifle with a quality hunting bullet. Just because it can get the job done doesn't mean it's the best tool for the job.
I am quite confident I could go out and kill deer with my .410 lever action and slugs. Especially if I keep it's limitations in mind. That doesn't mean I would suggest to everyone else that it is more than enough weapon and if you don't plan on shooting more than 50 yards you simply don't need anything better. That is just ignorant and not the case.
Oh, and the reason your family kills deer with shotguns using slugs is like you said, they live in Ohio and they don't have choice. I bet if you asked most of them if they could use a 30-30 instead they would.
Paul