Frankly, walking away for 10 minutes isn't much of an option when you have a load of people with connections to make. There are ways to start a hot engine just fine, but it does involve more than just trying a couple times with a two-step process.
I used to do 5 minute turns down in the Caribbean, and what usually worked for quick turns was this (TSIO-520-VB):
-Throttle full open
-Mixture full rich
-About a half second of prime (or no prime, personal preference)
-When the engine starts coughing, release the starter and briskly pull the throttle back to keep the RPMs down.
If that didn't work, you probably flooded it. Try the same above, except no prime, and try the mixture at idle.
If that doesn't work, do the purge procedure:
-Throttle full open
-Mixture idle-cutoff
-Mags off
-Engage the starter for 15 revolutions
-Mags on
-Mixture full
-Prime as normal
-Throttle cracked
I've never had a problem starting a flooded engine after the purge procedure.