The pump clearly cooled the bike just fine and can quite easily cool an FSAE car just fine with an appropriately sized radiator. Why the hell would you add the extra complexity of an electric water pump that's going to screw the power budget of your single's stator to design a cooling system to be absolutely 99% perfect amazing etc. Use the stock pump, it's simple it's there, it'll easily do the job you need. Run the engine with the inlet in a bucket and the outlet to another bucket to get an idea of flow rate.

Your cooling system design just needs to work it doesn't need to be the most perfectly designed thing in the world. Cooling systems don't make cars go fast, put your time into things that do. Chase the 20% gains before you chase the 0.2%. So long as the system can keep the car cool you'll be fine.