I am a player 1st and and a referee 2nd.
I am also a practical person.
In practice in your "dead ball" situation (T-Out) both teams will compete for position.
This happens ! And it's ok !
However, all the players must be aware that they are still playing to the rules.
For example, players are not allowed (just because there is a T-Out) to make illegal kayak tackles. Like wise, they are not allowed to hit each other with their paddles etc.
You say there is no GK, that may be true, but you can not stop a player trying to take up position of GK. This would be either Illegal Screen or Illegal Kayak Tackle - depending upon what and where you are doing.
During this T-Out, you can still be penalised and issued cards if needed. Also, if the ball was being retrieved on your side line and your team mate committed a foul on the opposing player trying to take up position under their goal, then your team mate would lose possession for your team as he committed a foul.
But this all means the referee is paying attention !
There you go - simple.
You know the rules - play to them all the time and don't rely on the referees and the game will be a lot better !!!