Your restaurant sounds idyllic.
Yes, you could do tri-tips like that. But I'd push top sirloin over tri-tip. You can cook larger pieces -- say 4-5 lbs at a time, rather than 2-3; and slicing is easier because there's no grain. You buy whole top sirloins and steak them at about 3" And, as I say, they'll run in the 4-5 lb region.
The whole thing is contingent on how you feel about handling steaks this thick on the grill. I find a medium temperature, or a hot grill start - oven finish works best.
Also, 3" steaks are thick enough to inject, should you want to go that route. As I said, I make a truffled barbecue bordelaise inject that does some very good things to beef. If you're seriously considering it, PM me and we'll talk. I don't want it all over the web.
You're going to love this beef marinade: Red wine / Worcestershire sauce 50/50. You can marinate anywhere from 20 minutes to overnight. The key is using the marinade sparingly. Use a little and it mixes with the meat's juices and makes a kind of syrup. The meat loves it. Anyway, once it forms a syrup, the syrup acts as a slather to hold the rub and lends a subtle taste. Naturally the longer the marinating period, the more assertive the marinade will be. And since both the flavors are extremely complimentary but neither overwhelms beef -- especially in controlled amounts, you can go for a fairly long marination.
My basic steak rub, which goes extremely well with the marinade is 12 parts Diamond Kosher salt; 6 parts smoked paprika; 4 parts coarse, freshly cracked best quality Tellicherry black pepper; 2 parts granulated garlic, 2 parts granulated onion; 1 part dried thyme; 1 part ground chipotle chile; 1/2 part dried mustard, and 1/2 part dried, rubbed sage. I imagine you've already got your own perfected rub, but you may want to try mine. Of course, the thicker the steak, the heavier the rub.
For my own group, I normally cook to 125F and allow a 10 minute coast -- which gives me another 7 deg internal. I think your party might be happier with 130F with 7 minutes going to 138F. You can finger test with tri very accurately but if you go with really thick sirloin, you're going to need your instant-read. Normally, I'm not much of a temp or timing freak, but this is an exception. I take a point and medium rare very seriously. Of course, you'll have to cook every fourth roast (or so) to medium-well for the trogs.
Slice thickness depends on presentation. With good tri or top you can go up to 3/4" per slice easily.
A variety of finishing sauces are possible. I'd lean towards a butter (as opposed to marrow) finish bordelaise (plus truffle oil), a bernaise, or a cognac/ cream/ mustard/ green pepper based on a stock reduction or a demi-glace. I remember you had something to say about demi-glace, but don't remember what it was.
I feel the same way about "Santa Maria" tri and top as you do about prime rib. Name the state of consciousness: been there, done that.
You could put a smoker in the back, but the hours are brutal. You'd need an overnight pitmaster.