starting hot Continentals
It's been a long time since I flew Bonanzas and Barons, but I remember their Continental IO-520s being much easier to start when hot than the comparable Lycomings on the Aztec.
Open the throttle just a little, select the mixture to Rich, turn the boost pump on and leave it on until the fuel flow stabilises on the fuel flowmeter, turn the boost pump off, select the mixture to Idle-cutoff. Now you can start the engine, and when it fires, smoothly advance the mixture to Rich. Works every time, whether the engine is hot or cold.
I think your IO-470 will start in a similar fashion.