Rather than rely on luck to get the games you want, or restrict yourself to custom lobbies that typically don’t fill up even past the halfway point, why not implement a lobby browser?
You can easily keep the option to quickly join a match. Implemented correctly, it wouldn’t affect the current flow or overcomplicate the menus, and would allow players to very easily find any populated lobby they want, rather than rely on fixed-rule custom lobbies.
Even better, it could offer information on what any given lobby will change to next and what round it’s on, preventing the frustration of joining just a fraction too late to get into the game and missing out.
Even EVEN better, if PGG has active moderators they hire, the lobby browser could well work alongside the report function and help with combatting the hacking problem.
The only complications I can really think of is how this might work alongside convoys, and also the implications of letting people choose what lobbies they want causing larger amounts of server traffic from the same number of players.