Don't think of them as gates, but paths. Move down the path, don't sit in the gate. Moving anywhere along the blazing white beam will give move bonus, so don't feel like you have to follow it all the way. You can move along it however much as you want.
During one of my turn hangs, I began clicking on a few of my fleets, and I noticed that one fleet that I had "passed", it let me move, and then it immediately cycled through the turn completion.
I think I have the opt-in update installed, it says [opt-in update] next to the title in the steam library window, and I flushed Steam to make sure. I still get random turn hangs, probably from the space pirates, as it even happened after turn one. Any suggestions?