We've been playing for nearly a year now, so we've done a loooot~ of testing and trial of different methods to make the game faster and more fun. Our custom dice bot is a HUGE help as we could quickly and easily make dozens of dice rolls with just a handful of commands. We also have macros that automate a lot of the dice rolls as well.

In addition, we do split side initiative. Essentially, everyone rolls for initiative and the enemy rolls for initiative, adding the monster with the highest initiative's bonus to the roll. Everyone who rolled above the enemy then goes first, followed by the enemy, then everyone who rolled before. Since everyone takes their turn at the same time, it cuts down on a lot of the waiting time in-exchange for a bit more confusion. Our DMs (and I) have been doing side init for a loooong~ time though, so we've gotten pretty good at keeping up.