No pic of your calculations...
What gears (final drive ratio) and, auto or manual?
If you have 3.21 gears and an auto (most common), I'd be hesitant to think 315/75s would be a good idea in the sand. It'll be hard on your trans (heat) with that gearing unless you go 4Lo. Also, if it's a 3.21/auto, the 315s will cause cruise control issues when encountering hills on your cross country drive which will make your trans miserable kickin' down all the time...a real killer. You can take it out of overdrive to combat a lot, if not all, of the downshifting.
The 305/70-16s (32.8") are very near your current tire set-up (32.6") as far as diameter so, it's a wash if you're not experiencing any current issues.
Consider that those numbers in parenthesis are "numerically calculated" diameters...a tire's actual diameter will vary depending on the MFG. The 315/75-16s (34.6") are a noticeable difference regardless who makes 'em.
Your Sahara originally came with 255/70-18s, (32"). Get a ProCal or other OBD plug-in to change the Jeep's programming. Your Jeep will want it for any tires that are not near the OEM's in diameter. Neither your current set-up or either of the alternative choices are allowing the vehicle to calculate things correctly. Everything - ABS/ESC/TC/etc. - uses speed as a factor when functioning. (Variations in tire size needs to be corrected as your speedo will read incorrectly.)
What's the real world difference when runnin' an uncorrected speedo?
The 315s will have you doin' 70mph when it reads 65mph. Not really an issue if you adhere to speed limits. Most of us seem to run faster on the highway. If that's you too, now you're in ticket territory runnin' 315s uncorrected.
Other things to think about on the highway are how difficult it can be to balance larger tires and what you're MPG will be.
Spend some time researching the brands of choice with respect to how well they balance.
A taller (numerically lower) ratio might be good for mileage when running stock sized tires. That bit of truth can lead people to thinkin' that an even taller ratio, due to bigger tires, will give better mileage. This is incorrect inductive reasoning. The taller tires, giving an even taller gear ratio, will make the engine work harder to push your brick through the air.
When it comes to tire choice, I use Tire Rack's online Tire Ratings to determine a subjective best tire for my use. I look for wet weather street performance and, if you click on the "off road" column header, it'll break it down into mud, rock, sand, etc. ratings. They have been my go-to for most of that kinda info but they don't offer every brand so I have to look elsewhere to fill the gaps. They, at least, offer a venue to narrow down the choices.
Good luck, and go make an entry in the Intro forum. Like, who the hell are you anyway?