Having a large party is always hard because you're bound to run into troubles. How you handle it depends largely on what you decide to change.

I want fewer players

Split them up into two groups. Give them a reason to split, different tasks towards the same goal and get them together again before the big finale. This is probably the best option and will benefit all players, but it will also be more taxing for you and might make scheduling sessions hard. I've been in a few games like this and it works out well, as long as the GM makes it work.

If scheduling is a problem, let them play at the same time. Switch between groups every half hour, let them interact at times and always have them reconvene before a boss fight. This is hard and time-consuming and it will probably not be the best option for the players. I personally hate waiting while others do their stuff. :-)

I want to speed things up

Don't allow the players to meander off too much. Keep your adventure tight and focused and when someone wants to check out something irrelevant, don't let it get drawn out. You don't have to cut all dead ends short, but let the players know fairly quickly that there's nothing to gain that way. Same about locations. Don't walk the players through a detailed map if all they need to do is get on with the adventure, just tell them they explore the rest of the town and give them some general information.

I've sped up my games a lot by being more clear and not let the players work too hard for the price. I also played in a game where the GM wanted us to get into an isolated town. Instead of waiting for us to spend a lot of playing time come up with a perfect strategy, he simply let guards discover us outside and assume we were citizens caught in the blizzard. Welcome back in, hope you didn't freeze too much. Done.

I want to keep the odd player occupied

Branch off the adventure into small branches that quickly join together again. Perhaps they need to force info from someone or take care of a troublesome person. While the odd-man and a few others are off slashing monsters for a piece of the clue, the rest can enjoy bickering about who sleeps where or what color the get-away carriage should have.

If my players splits up (and some players like to split up...) I always try to maintain two threads at the same time. Before I GM one of the groups, I make sure the other group is in a place where they can RP freely.

I want to cater to both sides

Try alternating your pacing. Let the players dawdle on for one session, then give them a time-limited task and set a timer IRL. The more time they waste on side-tracking, the less likely it is they're going to make it. The timer should be visible at all times and they should be aware that it's a problem if they let it run out.

I want to keep everyone happy

Buy some cake and talk it out. Seriously, set aside one session, bribe the players with some fika (https://en.wikipedia.org/wiki/Fika_(Sweden)) and discuss in the group how you can make sure everyone gets what they want from the game. Make it clear that it's not about accusing anyone, but that it's a way of bettering your experience as a group.

I early got into the habit of asking players for their input after a session. Not individually, but as a group before they leave for the night. This way the group can talk amongst themselves and by asking good questions you can get them to work out issues together.