I don't have time or inclination to brown it first, so start high temp? Any idea how long these usually take? I want to know when to begin testing it.
Just a fyi, I roasted it at 450F the entire time, got some browning. 30 minutes might have been ideal but I have someone who doesn't like med rare. 40 min put it over for me, except the very thickest part. 35 min would have been ideal. I let it sit out an hour with Santa Maria style seasoning. Didn't have more time than that. We enjoyed it.
Rather than minutes/hours per pound I always go by internal temperature which should be 130F, then it gets a 10 to 15 minute rest. I prefer to cook outside over real would charcoal but this isn't exactly the weather for that method. Because of the shape of the tri-tip you should end up with rare meat as well something closer to well done or medium well.
Pay attention to the grain when it is uncooked, as you will want to slice the cooked roast across the grain to keep it from being tough.I love the beefiness of a tri-tip, but have cut is wrong on occasion and regretted it . If you opt for the rarer time and temp,you can always serve this on hot plates for those wanting it more well done.You can't undo an over cooked steak ; a Tri tip is simply a really thick steak.