This is not a solution, as it requires previous communication between players (and this is an issue for casual players, as I also think that most of them don't use discord or are even in the pdx forum), but may help some people to give it a try: matches with partial lances. Why? Most of the matches take at least 40 minutes, some even the double. I'm sure that some players can't (or don't want to) spend that long straight in a match. Well, even sometimes it's why I don't play much MP these days (I have around an hour or less to play, and I usually have my doubts about being able to find someone to play and finish the match, so I play single player). If, instead of 4 'Mechs each, it is 2 or 3, the match would probably last less. Main problem with that: maximum c-bills (probably would require another match setting option with less money). So, long story short: an option for quicker matches may attract some players.
Although, for some days with planning before, I would love co-op multiplayer games (as I mentioned elsewhere), I think that having 4 or more players connected at the same game would be problematic, at least with the server issues (if it haven't improved in the last week).
Tournaments, if there are not too many running at the same time, could also a good idea to attract new players and to get to know other MP players. Again, the problem is communication, how to let people not convinced about MP know about these tournaments? And I believe it would be wise to do it without "annoying/spamming", particularly for the single players that seem to have some sort of grudge against MP.
Sorry for not providing much of a solution, but I hope that by rising a few problems I believe are affecting the MP community (which is a bit in a standstill/stagnate), we can find solutions or suggestions for the HBS team (the most structured and organised, the better).