Many thanks Toritoribe, your post really helped me figure it out!
To summarise what I've found for the benefit of anyone else reading this:
The 連体形 and 終止形 are further discussed at
this stackexchange page.
抜け出す is acting in the 連体形 form, modifying the phrase には .
The pattern being used is:
[Verb] には [Adjective]
Apparently the adjective is usually いい , and in this case the phrase means "good for doing [verb]".
Returning to the original sentence:
こういうみんながこわい状態から、みんなが
ぬけだすにはどうしたらいいかな?
It seems a fair translation would be:
What would be a
good way for everybody
to break out of this state where everybody is afraid all the time?
Of course, I'd welcome any comments improvements on this, however.