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Which programs outside the South have a reasonable shot?

Not many. When Oklahoma and Ohio State are struggling to compete the rest of us face a steep climb. 

I predict Clemson will fade after Saban retires.

Yeah, UGA that year was 4-12 in SEC play.  A tornado whipped through downtown ATL during the tournament stopping one game.  UGA won four in a row at the tournament to make the NCAAs.  

https://en.wikipedia.org/wiki/2008_SEC_Men%27s_Basketball_Tournament

During overtime of the Friday night quarterfinal between Mississippi State and Alabama, a tornado hit the Georgia Dome at 9:40 p.m.^[4]The National Weather Service had issued a tornado warning at 9:26 p.m., because radar indicated a thunderstorm capable of producing a tornado.^[5] The storm tore open a panel on the north side of the dome; sheared bolts and insulation fell into the arena. After the storm passed, the teams returned to the court at 10:30 and completed the game.^[4]

Georgia, which had a sub-.500 record going into the tournament and had to win the title to secure an NCAA Tournament bid, was forced to play and win three games in the space of 30 hours, including two games on Saturday — the original quarterfinal game against Kentucky that was postponed by the tornado and venue change, and the subsequent semifinal game.

Is it odd that I find pride in Florida's apathy about basketball?  We won back-to-back NCs in hoops and it's like:  cool, how's the football team doing?  
Having NCs in football, basketball, and baseball, all within 10 years is pretty cool, though.

I watched Florida win the football NC in Glendale, Arizona in January, 2007 then watched them win the BB NC a few months later in Atlanta, Georgia.  As an Ohio State fan it was frustrating to lose both to the same school.  If you think about it, it really shouldn't be.  Ohio State's accomplishment of making the CG in both in the same year is a phenomenal achievement.  AFAIK, only Ohio State, Florida, and Oklahoma have ever done that (I could be missing somebody).  If Ohio State had lost the CFB CG to a football school that typically sucks at BB (say Bama) and lost the CBB CG to a BB school that typically sucks at FB (say Kansas) it would have felt a lot better, LoL.  

Yes, and a lot of that depends when you were born, in comparison to how your school has done during your viewing lifetime.
I may be among the worst "mighty" Gators fans, because my viewing lifetime began the same year Spurrier started at Florida.  My few college football memories pre-1990 weren't necessarily of Florida football.  
So I've seen all of UF's NCs, 2 Heismans, all of the SEC titles, and a top 3 program overall, nationally.  So that's my baseline as we inch forward.  Yes, a 9-3 regular season being considered good or over-achieving feels odd.  

Didn't a completely mediocre UGA win the SEC tournament a few years ago and make the field as a 14-seed?
And "only" one Final Four is still better than a lot of schools.  Current #1 Tennessee has zero (and just one Elite Eight if memory serves)

I wouldn't say better than a lot of schools.  You are correct, Tennessee has never been.  2nd most NCAA Tourney appearances without a Final Four, behind only Missouri.  Alabama, Boston College, Texas Tech, Vanderbilt, Arizona State, Texas A&M, Clemson, Miami and Virginia Tech are some other Power 5 schools with a decent-ish history to have never made one.

Is it odd that I find pride in Florida's apathy about basketball?  We won back-to-back NCs in hoops and it's like:  cool, how's the football team doing?  
Having NCs in football, basketball, and baseball, all within 10 years is pretty cool, though.

I find it infuriating, Lol.  Florida clearly is a football school but has 5 Final Fours and two national titles in the last 25 years.
Michigan and Ohio St also have solid basketball traditions where football is king.