Too much of a long shot for what?
What’s your top choice.
If you say UGA - i’d ask - then why are you saying you are trying to avoid the SEC.
In my mind, if you are interested in not just journalism, but advertising and PR, then Bama should be right up there with UGA. Cost wise - you’ll get $24K off but if you can get your SAT up 10 points, $28K off. Worst case though, you are upper 20s all in.
After Bama, I’d say OU.
Both are SEC though - as is UGA.
That’s just an overall - if you had journalism, PR, advertising - it doesn’t mean you can’t make it happen from anywhere else because you can - from everywhere else.
But those schools have the reputations in all three categories - but reputation isn’t really a huge driver there.
I listed others that could work.
btw - i’m not sure there’s a huge difference between say - Clemson and an SEC school.
Elon, of course, a very different type of school - also great.
I don’t know if you get into UGA/UF but you’ll get into a lot of great schools.
And your schools were fine - they’re just not known for the areas you brought up vs. others I mentioned.
Whatever you do, make sure you double major…communications grads have it tough. I went to Syracuse and maybe it’s different today, but easily 80%+ of kids had to pivot in life to something else.
As for Bama, my engineering kid went. He tried to party once - and that didn’t work out for him 
You can make any school as you want- and again, all the schools have your majors - maybe just not the breadth of offerings or successful alums. Most at Bama are not in Greek life btw - so like many schools, you are far from alone if you’re not. In fact, you’re in the majority. But - that said, yes, the houses are gargantuan and that makes an impression on many.
I’m not sure Ga Southern is different btw. And UTK definitely isn’t different.
For more chill SEC, you can look at MS State but I think advertising and journalism are housed in separate schools there.
Truth is, a lot of your top J / PR / Advertising schools are the big flagships - and in many ways, they’re similar. UGA/UF/Bama/UTK are interchangeable for what you don’t like about Bama. Auburn and MS State maybe a tad less but then a lot less “ranking” wise in areas you desire. Maybe OU is that in between but more like UF/UGA/Bama. A Syracuse/Miami will likely be over budget. Hofstra is suitcase but will price greatly.
Maybe Elon or Butler are that type you are looking for.
Getting out of the SE at big publics, you could look at Indiana (maybe above budget) or Minnesota. Ohio U would be another that could do well for you but if you choose advertising or PR has only a minor. But it’s well known for journalism.
Staying in the SE, in addition to Ms State (well known for weather journalism), maybe UCF and to a lesser extent USF could work for you.
Really - you can go anywhere and be a journalist or get into advertising/PR. Two of the top sportscasters today are SU alums from my era. But then the next two - if there’s a big 4 went to Beloit and William Paterson…that’s sports because I know it…but if you look at the bios of newscasters, they come from literally everywhere.
A school like UT Chatt might suit you - but I’m not sure you get the “breadth” you want access to - especially if you don’t know your area of focus. That’s where the big flagship might help…but ostensibly, reputation aside, if Bama bugged you, I don’t see how UTK, UGA or UF are any better.
@Bill_Marsh brought up schools you wouldn’t normally think about for journalism per se - but again, you can go anywhere - so maybe you should think about the type of school you do want. What was suggested are more liberal arts types and smaller. You listed a bunch of big ones + Elon…but maybe you saw them on a ranking. But have you thought what you’d actually like / want in a school?