Thanks for the advice, and I have been doing that, but now I am technically in 5 games, and the limit at 20 phases is 4. Will I be able to join new games one I hit 20 phases even though I am technically in 5 games currently.
I guess my real question is: Does joining an open position count towards your game limit?

I'm not sure. It's been a long time since I've been a new player, and I think I started relatively slow so I didn't run into your problem.

I am relatively sure that open positions you take don't count towards your games played (you also don't have a bet amount for them, but can win points).

I guess I will find out soon, I am at 18 phases. Will post results here.

So I am currently at 20 phases and I have read the rules more carefully. It says that 2-player games do not effect the game limit, and there is not mention of joining open positions effecting the game limit. I am currently in 6 active games, 1 of which is 2 player, and 4 of the other 5 are open position joins where I will very soon die. I am not able to join any new games.
I assume this is because open positions ignore the game limit requirements for joining while still counting toward your total number of games. Is this known and intentional?

This is exactly how things are working for me right now. I have several games I'm interested in joining but can't due to game limits, so I'm "spectating" them, kind of as a bookmark and also to check which ones are likely to start soonest. Then to achieve the minimum phase requirement I'm sending 2-player challenges to farm phases (currently at 26 in just a couple days).