I think I found a way to get consistent 20-30 minute private lobbies.

I don't know if this has already been discussed on this sub before, but I figured out that after doing either the Gault, Hoare, or Roach infamous bounties in Saint Denis you can get into a lobby by yourself for about 20-30 minutes fairly consistently. Usually I play solo so I don't know if this works if you're in a posse, but I can't imagine why it wouldn't. I usually use these lobbies to do trader deliveries without the fear of griefers, but I've noticed that sometimes I can stay in these lobbies for up to 50 minutes if I don't do any missions and just chill in free roam.