Thanks so much for trying it out!! When things start getting really busy, I have to restart even with lots of hours of play. (F4 is a hard restart, btw. :-) and ‘r’ is alternate respawn key.)
I found that my best bet is timing it for a slight nudge when it’s early and things are slower and either a careful slow walk or sometimes a mad dash of speed either into or out of the pen area, but if things go wrong and a bunch appear then who knows! might get lucky?