As to the question of whether friends and sister would keep texting after Suzanne let them know of her problems and her fear, I'm not so sure.
My controlling ex would have been asking "Why all the texts?" Even if everything was on silent, he'd have wondered why I was looking at my phone (and did in fact wonder that - I saw it in one of his journals after we split up - but by then, I had let a bunch of people know that if anything happened to me, well, I had shown them where I kept the only photographic proof of his abuse and where I kept my own journal).
Controlling husbands often resent any form of communication with someone who is not them - sometimes, even with a woman's own children (my ex resented attention given to our own children, and we had to arrange meal times so he ate before the kids got up or after they were in bed - he got too snippy with them and no one could digest properly, otherwise).
You are absolutely right.
And that would have been an obvious thing to say and consider. But he couldn't say it out loud, because no one voluntarily leaves Barry (and probably, no one does anything in that family without Barry's approval).
I'm guessing he's stuck with stranger abduction when he lied to the girls (and I bet he didn't bring the situation up very much after the first month of Suzanne's disappearance).