Cooking a nice pan seared steak for picky eaters
The method you describe should work, timing wise you have it about right, except it will need longer if you are aiming for well done. Salting and oiling before cooking works well, as does letting the meat come up to room temperature (if you are aiming for rare medium-rare a cold steak isn't a bad thing as it lets you char the outside more while having the inside less done).  Maybe you're better off leaving garlic out unless you know that's their taste. If they don't like fat adding butter may backfire on you, plus, butter and garlic can cover up the flavor of the steak that you want them to enjoy. You know your family and what they might like best, it's a judgement call. 

The thing you are missing is that a steak doesn't have to be a monolithic thing, and by treating it that way you miss the opportunity to have something the way you like. If you have 4 steaks then cook 3 medium well to well and cook 1 to your taste, if you have 1 steak cut a quarter off and do the same thing. They don't have to eat your steak and you don't have to eat theirs. 

A couple of things:


Don't trim fat before cooking as you will end up with a dry steak. As you plan to serve it carved trim the fat after cooking as part of the carving process
If fussy eaters don't like the look of food raw they won't eat it cooked, so keep them out of the kitchen if you can