Six players is a lot, but it's not too many. If everyone cooperates, turns can go very quickly.

Most of the delay is from players not paying attention and formulating plans when it's not their turn. Then they have to be brought up to speed, come up with a plan of action, and then do it. Ideally, they should launch right into the action as soon as it's their turn. Players who are really on top of matters can start even before it's their turn.

Get a set of these: https://www.amazon.com/gp/product/B01LYV8RDT/

Excepting the need for DM to provide the player with information, if a turn can't finish before the sand runs out, that character is taking the Dodge action for the round. Naturally you can suspend this house rule as you see fit, or rather, you can decline to enforce it.

Also, don't just announce whose turn it is, but whose turn is next. That way they shift mental gears from observing the action to deciding what they will do.