Modded servers!

Instead of making people with mods search for private lobbies/matches, instead make supported server for modded players, like a launcher, when they start the game it would ask if it wants to play the vanilla or modded, upon selecting modded they would be put in the modded servers. On which clicking to find public lobbies, they would only que with players who have mods installed to make easier for search for matches. 

It's hard to find people making modded servers on your region, so most will be forced to play with 200+ ping (like me) if they want to keep their mods and being "forced" to play private matches.