I haven't played much Civilisation Multiplayer, just a few random games in Civ5 before G&K expansion. None of them were from the beginning. Most were 2/8, 3/8 games where i jumped into someones abandoned empire. In some ways it was quite cool to take a broken down Civ and restore it to some kind of credibility. At no point did i ever consider winning. Hell, the guys that were winning weren't really bothered with winning,

One game i jumped into was 6/8 and that was pretty cool, i think it lasted 2 whole Era's before it started to breakup(somebody got there butt kicked

) but it was the only game i played with any Player Vs Player competition. One of the games i played i did not see or interact with any other player outside of Chat. I asked if they wanted to go to war against an A.I Civ that was between us and he declined, preferring to just work on his Civ. It was surreal.
You want people to not quit. My experience in multiplayer is that "quitting" was the core part of the experience. You just bounced around multiplayer matches looking for interesting Civs to play, almost like browsing the internet. No one really cared about winning and none of the games i played had a player stay for the whole game.
Civilisation Lobby Multiplayer is a strange beast, I mean how many other games out there needs a 7hr commitment just to see who wins, at that is on quick(I absolutely abhor quick

). Asking people to sit through 7hrs straight and being penalised if you leave would make Multiplayer even more niche then what it already is. Civilisation from Ancient-Information is not really made for random competitive multiplayer. Lockouts might work for Dota, but those games last 90mins, not 7hrs. Asking people to sit through game for 7hrs, when they are losing or not enjoying themselves is just sadistic, good luck getting people to actually play. The solution to this not really developer side, outside of giving us shorter ways to play, such as scenarios, Era Games etc.
Your best bet is to join those communities such as no quitters community. Or maybe you want a community that encourages "quitting" where members take turns in guiding a Civ against the A.I (or Team-based-multiplayer). I'd enjoy that as a Random game of Civ. You pick a couple of Civ's you like and you go into a queue where you get 50 Turns on Epic or something where you share control of the Civ with other players, who can also watch as you play. I read a PC gaming Magazine article where the writers did this for Civ 5, sounded really cool and i think it would work for Casual Civ.
The only thing i have heard about Civ6 Multiplayer is that they are revamping it with a focus on shorter scenarios. I think it has to go bit that way in regards to competitive multiplayer. 7 hours is just too long. Think Dota, Battlefield, Counterstrike et all. They all last 30-90 mins tops. You can log in and get a result in smaller timeframe. By all means still have the full game experience with lobby, hotseat and pitboss etc, but give the competitive multiplayer's an option that doesn't demand a 6-7hr commitment.
I like to think Civilisation Multiplayer is similar to Test Cricket Vs One-day Vs 20/20 Cricket. Test Cricket might be the purist form of cricket, but not everybody has got 5 days to wait around for a draw

Hell, even 1-Day cricket is too much of a time commitment. Hence the birth of 20/20 Cricket whose timeframe now is the same as most sports. You can have tense competitive battles or epic long saga's. I am not sure if you can have both at the same time and appeal to the majority of players.