You're looking at Ohmwrecker completely wrong. It isn't supposed to be used to stop damage and start a dive - activate the effect, then dive in and try to do something in that 3 second window. You are supposed to use it near the end of a dive, or sometimes in the middle.
The real power of Ohmwrecker isn't "Oh boy! I'm going to stop 3 turret shots!" The power comes from the aggro reset at the end of the effect. You use it at the end of a dive so you can immediately start focusing the tower without having to walk out of range and then walk back to start attacking it. You use it mid fight to force the turret to switch targets when whoever is tanking it gets low. You use it to save allies who get trapped under the turret.
If you look at its stats, Ohmwrecker is clearly intended for tanky champions, not assassins or divers like you're talking about. It's intended as a tower dive item, plain and simple. Not for splitpushing, and not for solo tower kills.
Get one or two allies, build up a decent minion wave, and dive the enemy under their turret. When you're close to killing them or forcing them away (or in order to force them to leave the turret), activate Ohmwrecker, finish them off/drive them away and take the turret while it goes back to targeting minions.