The issue with that is that tornadus is in many ways a wallbreaker, so it wants to come in early, mid and lategame, something that stealth rock inhibits. Its counters and checks are defensive enough to last the whole game, so I don't feel as if a lategame sweep should be the largest goal.
thing about it's counters are they're so far and in between. It's main counters are Chansey, Blissey, Jirachi, Tyranitar, Heatran, Bronzong and Magnezone.
Chansey & Blissey - Only 3HKOed by Focus Blast, can Softboil off damage, paralyze or poison Tornadus ending it's effectiveness, excellent counters to Tornadus. however uncommon.
Jirachi - Sp. defensive Jirachi takes about 40% from each Hurricane. only recovery is Wish, which gives a turn to go to your Jirachi counter. needs wish+protect and avoid confusion hax to truly counter Tornadus.
Tyranitar - Takes away rain and afterwards, tanks Hurricanes even if they don't miss and OHKOs with Stone Edge. Tornadus has to rely on U-Turn and the terrible Focus Blast to kill it. good counter, but lack of recovery ruins it's staying power. Rain teams should have Tyranitar covered anyway.
Heatran - Can take Hurricanes sure, but not Focus Blast. Without HP Ice can't do much to Tornadus in return except for sit there or Roar it out. not to mention that heatran is neutered by rain anyway
Bronzong - rare and just too passive to be as good as it could be in OU
Magnezone - also can't take Focus Blasts but aiming for a Focus Blast when there's a chance it'll miss and you get KOed is a bad idea. however, it's a niche steel trapper. not what I think of when someone says huge staying power.
so apart from the blobs and specially defensive Jirachi with Protect, I don't get what you mean that most of it's checks and counters are defensive enough to stay the whole game.
in addition it goes against what I just said about not needing a spinner, but if you do run Dugtrio with it (who does need a Spinner to be effective) Dugtrio shuts down all of the above pokemon apart from Bronzong and Jirachi with U-Turn.