A diverter tool reduces surge pressure when running casing into a wellbore. The tool is kept open while running the casing so surge pressure can pass out a bypass port. The tool is then closed with a ball that lands in a seat disposed in an interposed condition in a sleeve of the tool's housing. Fluid pressure applied against the seat in the interposed condition engaged with the ball overcomes a first fixture temporarily holding the sleeve open. The fluid pressure shifts the freed sleeve closed. Additional fluid pressure applied against the seat with the captured ball then overcomes a second fixture temporarily holding the seat in the sleeve. Once freed, the seat with the captured ball pivots from the interposed condition to a stowed condition to expose the internal bore of the sleeve to the longitudinal bore of the tool so additional cementing operations can be performed.