Why not 5.56? Is TX one of the states that has some retarded law about .224" projos not having ENOUGH DEATH POWER?!!?!?
Just put together a 14.5" pinned 5.56 carbine or middy upper with a 2MOA T-1 and you'll have a super lightweight carbine that can hit a deer's vitals to that range no problem and we all know it has a pretty flat trajectory in the lighter weight bullets. Toss a 3-9X on there if you require it.
300BLK is great if you're running an SBR but isn't worth the cost in a full length gun IMHO (you don't get enough out of it over 5.56 to justify the 2-3X cost in ammo). If you really feel you need MOAR DETH POW3R!!!11! then sure go with a 6.8. At least that ammo is on the shelf at Cabelas.
A hole is a hole. As a "for instance," 300BLK is 30-30 from the AR platform. Anyone who doesn't think that a 30-30 will get the job done on a whitetail is ignorant. Just pick whichever one tickles your fancy and then make sure YOU are up to the task of making 2-3MOA hits at 300 yards with it (you only need to be able to hit a 10" circle, after all).
All that said, if I ever see a whitetail at 300 yards when I'm out with my 8.2" 300BLK, I'd take that shot without reservation and I'm sure it would be as tasty as one killed with 5.56, or 6.8, or 270, or .338 LM or...