Cooking a nice pan seared steak for picky eaters So here's the situation:
I love a tasty steak. I also have really particular family. If the meat is not cooked all the way (aka very little or no pink left) it's still partly raw and no one will eat it. If the meat has globs of fat on or in it, they dissect it and remove them. My Mom buys steak on the principle of the less fat you can see, the better meat it is (and is therefore convinced that more expensive steaks are worse, not better, and not worth the outrageous price). Obviously, my goal is to convince my family that this is not true, so we can have some better beef sometimes. They like delicious food, so I know they'll still love the taste of good beef, IF I can work around the aforementioned roadblocks. After much pleading, I convinced my mom to get to some better steak as a treat for me. She brought me some NY strip (what I asked for), though it's thin cut (it is a bit under 1/2 inch thick, I think). I'm hoping that the thinner meat may actually work in my favor, since it has to be medium well to well done anyway or no one will eat it. 

So, a lot hinges on the results of the meal I'm cooking tomorrow, and I want to get it right. After much internet research, here's my game plan:
Remove steak from fridge about an hour before cooking, pat dry and salt it. 
Heat a thick bottomed stainless pan to super hot (we don't have cast iron).
Dry steaks off well, coat them in canola oil, and put in the pan. Sear a couple minutes on each side. 
A few minutes before finishing, add some butter and minced garlic and spoon over the steaks while they finish cooking.
Take em out, discard the garlic, let them sit a few min while finishing other meal prep stuff, and then slice them up in thin strips (against the grain, of course!) and serve them.

Am I missing anything? Anything else I should know? Thanks!

P.S since I haven't cooked with these before I'm not sure about all that fat my mom is so offended by. I know the marbling makes the steak tender and juicy, but will it cook down somewhat and be less "present and offensive"? Or if I trim what's along the edge before cooking to help avoid complaints, will it ruin the way the steak cooks? Any help here on how to still make a still pretty tasty steak that my family can't be overly snobby about is welcome!

Also, please: if the only thing you have to say is "if you're going to cook it near well done then you're ruining it anyway, so why bother?" DON'T. It's not helpful unless you also have some nice tips on how to make a more thoroughly cooked steak better.

UPDATE: Steaks were actually closer to 1/4 in upon closer examination, and so they cooked really fast. Ended up a bit overdone even for what I had in mind. BUT they still tasted much better than what we usually have, weren't noticeably fattier after cooking, and even overdone weren't as tough as some of our usual beef. I got more compliments than complaints and they seemed to be a hit, so I consider this one a win. My brother said it was the best thing I'd made since I took over most of the cooking. :) The only thing I did differently from my original plan was I cut back on the amount of garlic I used, since I didn't want to overpower the meat's flavor too much, as someone pointed out in their answer. Thanks guys!
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