My tips:

1. let dice make decisions, and don’t try to explain them. Quickly number reasonable targets in a standard way (I do left to right, top to bottom), roll a die and move on. Get it down to less than five seconds.

2. it’s better to be quick than to be optimal. Get the attack out and move on.

3. enemy spell casters have three or four rounds to live. Mostly they fire their biggest blast in the first round or two, and then they’re trying to escape. Maybe they buff an ally or two, but that’s advanced strategy.

4. You handle a combat one step at a time. Work your way down the list, and each time its the same simple decision: which attack? which target? what result?

5. Sometimes combat in D&D is a grind. Go easy on yourself. Keep calling out the results, and the players will understand.

6. Six players is a lot. Delegate work to them, especially when they cause it (e.g. bane, or damage that ticks after their turn. ) it will keep them engaged.