First question to ask yourself: Is this the only reason for your growing case of DM burnout? If so, that changes the importance of the issue. It is because you see it as a negative motivator? In other words, you feel like you work hard on the game, and the fact that your players aren't paying rapt attention feels like a slight, or you worry that it reflects on your DM skills?
I think a compromise might be in order. For my group, we like to balance the two. The joy of D&D and gaming is that they are social activities, usually with your friends. It would be a dour endeavour if the game were without some diversion or socializing, and I doubt you want that. However, there is a line that can be drawn, fuzzy and blurred though it may be.
My group gathers on either Friday or Saturday from 7:30-8:00 to about 1:00AM, so I understand where you're coming from. Sometimes we are very late to start...I know, I can be part of the problem, myself. Talk of the latest movie, Weird AL album, Everquest, Queer Eye for the Straight Guy, or anything else goes. But when the game is in full swing, the rules change.
Try to see if you can convince folks to get it out of their systems in the beginning and end of the sessions, for a start. Slightly unsubtle reminders during the game can help. For example, in our group, if we're getting too far afield, I or a player may point out "...but that's not really important right now, what spell are you casting?"
Keep rulings short and simple, and deputize players in such instances, unless the rule is a gamestopper. For example, when a player wants to use rusting grasp on a golem, and you're not sure how to rule, or he wants to grapple a roper...let them find rule cites for you, or relevant text passages. This occupies them, and frees you up to keep the game moving. With 8 players, you have 2 more than I do, and have a lot to do.
Try to minimize instances where parts of the party have to split up. In a game with as many players as you have, if only four players are busy, the others will invariably fall to discussion if they are unoccupied by the game. If this is unavoidable, either find ways to utilize them towards the game (such as rolling for monsters or researching rules, finding minis, etc.) or at the minimum, ask them if they can keep it down so that it doesn't disrupt you, so that you can get them back in the action quicker.
Ultimately, you need to do what's the most fun for you and your group. There are lots of approaches to take, and ways to do it.