When to put new ball into play after HR?

[Bluefoot]

I did not want to hijack the BR missing Home Plate after a HR thread, so I'm starting this new one here.

When is the proper time for giving the defense a new ball after an over the fence HR? The pitcher usually asks for one right away while the runners are still circling the bases, as they are usually anxious to move on with the game. But I always wait until I've watched all runners attempt to complete their running of the bases, and the BR has passed home.

The reason I bring this up is the aformentioned thread, where the BR fails to touch Home Plate, and if a new ball were put in play, that could lead to some confusion, if the new ball were used to appeal the BR who had not yet entered the team area.