Re: 6.5G or 308
With the current state of availability of ammunition, magazines and parts, this isn't exactly something that you can simply read into old threads for the right answer. This is a web forum for interaction, not a library for research alone. It's comments like above (not you SW, the other ones) that hinder the growth of our sport.
OP, I would recommend turning yourself towards a heavy barreled .223 upper, SPR/DMR style. Magazine and ammunition availability alone is why I recommend that. Barrels are still out there and available. Keep checking for Fulton Armory to come back online as last time they were, they had several good Criterion (by Krieger) barrels that will shoot quite well. There's other sources out there too, just keep your eyes open and email notifications will help as well. Most folks are looking for 14.5-16" barrels, so if you're sourcing a 18-20" you may have better luck finding one sooner than later.
Punching paper or ringing steel doesn't require the heavier hitting or ballisticly superior calibers if you aren't going past 600yds. Wind cheating differences inside that range is a moot point as well, and I view it as better training if you aren't competing anyhow.
You're already shooting .223, so you have the brass. If you're not already, get yourself a simple reloading kit to start into that. Ammo availability isn't that great now, so I would try to stick with what you have.
As for hunting, well I know the deer aren't all that big in the panhandle, so with the right round and proper shot placement you can easily hunt with it as well. Anything bigger, well that's where the .308 would come into play so consider your application there.
My answer may be totally different next year, and last year I would have said go .308 for more game taking versatility yet having a commonly found caliber, but in my opinion the current state of affairs don't allow for that right now at a reasonable value.