What we're saying is you don't need time for all that. You only need time to hear it. If you hear it before the player catches the ball, but you verify it as he's catching it (or even after), you can blow your whistle (respond to it) after the shooter has it. We do this all the time with timeout requests.

Coach calls timeout just before the defense gets their hands on the ball and ties it up. You give him the timeout because it happened before the held ball.

Coach calls timeout just before his shooter releases a try. You blow the whistle while the shot is in the air.

Coach calls timeout just before his player releases a pass. You blow the whistle just as the defender catches the pass and starts running down court.

This play is no different.

Just because it was requested, doesn't mean it is granted. I may or may not grant a time out in these situations, depending on when I heard the request, verified if needed, and checked the status of the ball.

If I hear it when it's allowed to be granted, I'm granting it regardless of what happens between that moment and when I blow my whistle.

I really don't know any officials who do it differently.

Truly, it should ONLY matter when you heard it.

Is it no longer a foul if you don't blow the whistle while the contact is still occurring?

If you're taking a lot of time to do these things, you need to increase your awareness and recognition skills, IMO.

I don't take a long time, and don't always have to check status of ball, or look to see who called it. I know there are times when a time out is coming and I am aware of them.

I think you completely missed his point. The amount of time you take is irrelevant.

Oh, no. Not this again.... :D