So I found this. It's good for people with an XB1 who want to do CEO work in peace and don't have any other way to get a solo public lobby without having a mile long cable running through the house.
It takes a few minutes but I tried it twice yesterday and it works, it's much better than swapping sessions for ten minutes and crossing your fingers.
1 - Make a playlist with one quick race. Down the Drain is probably the best since it is short and spawns you in the city to shorten travel time. You could use Criminal Records if you want to spawn in Blaine County instead.
2 - Do the race.
3 - Press X to restart the playlist.
4 - Quit when you get back to the lobby.
5 - Voila.
Notes: If you start from an invite or solo session, the game will think you aren't in a public session even though it says it you are. Thanks to Semaj 2JZ for pointing it out.
If you also want to stock up on nades and stickies and molotovs while you are at it, then use Gridl0kk's Fill 'Em Up race here. It will spawn you in Blaine County. Thanks to Jenkiiii for suggesting it.