From the original logline, I got the sense this was a siege movie - a la Assault on Precinct 13 - where the survivalist and his cronies need to defend their compound? But it sounds from the comments and suggestions that it's been pushed more toward a road movie - get to the compound, be safe?
FWIW, I really dig this idea (how does Bear Grylls fare in the Mad Max universe), but I think the original feeling -- defend his private compound with the help of fans that have come to see him as their savour -- works better for me. I'm more likely to watch that than another 'traipse across the post apocalyptic landscape for the safe place' narrative.
RE: character growth. An easy way to imply it is through the character's flaw. It's a single (or very few) word that tells us what the inner arc is going to be. In this case, you've described him as immoral - which tells me the arc you see the character going on is one where he learns morality, and the need to life a moral life. Which I think works.
I imagine that if you've got a world where a survivalist who was rich and has his own secluded compound, where his fans have flocked to live by his example, and he's treated like a king or the messiah -- then the easiest thing to do with his character is make it that he's actually NOT as brilliant a survivalist as he made out to be. That he's a fraud -- his amazing skills were all scripted. And during the attack (and perhaps abandonment) of his compound from outside forces, and the fact that he has to protect all of the people living there, the reality will come out. This guy is a huckster. But eventually, he'll have to use what he DOES know to protect the people he cares about. It's got a whiff of Three Amigos/Bugs Life/Galaxy Quest about it. (All great movies).
I haven't commented on loglines in a while, because often it's draining saying the same things about what's wrong with loglines over and over. But I have to say, polished logline or not, this is a great concept and I'd like to see it. It's familiar enough that I can understand and envision what it is, but fresh enough to be something new. Good luck with it!
"After the collapse of civilisation, a charlatan ex-TV-survivalist and his acolyte fans defend their mansion fortress from a band of bloodthirsty bandits."