Here’s what I do:
Keeper saves the ball, has it safely in his grasp. Probably like everyone on the pitch (at my level, at least) I’m glad to grab a breather, and, like everyone, I’ll jog to take up my position (on or near halfway line) and when I’m in position I’ll start my (mental) countdown of six seconds. If keeper still hasn’t released ball by then I’ll give him a shout and he’ll, inevitably, release the ball. I can’t, from memory, recall ever penalising a keeper for this offence.
I be right under the LOTG, I may be wrong, but what I am is consistent. Nobody bats an eyelid to the above approach in the first minute of the game, there may be complaints in the last minute of a close game, but if I’ve done the same all game then I don’t see why I should change my approach just because one team desperately needs a goal.