The 706's are not an issue - small chamber to keep up the compression and flow just fine until you get over 7500rms with a 5.3. I'll guess that you don't plan to be spending much time in the 8000rpm range? Correct me if I'm wrong. An LS has two distinct advantages over anything built before it - the bottom end can withstand 7500rpms in stock form with 200k+ miles on the odometer, and the stock heads flow almost double of anything old school Chevy or Ford for the same displacement.
If you want to make silly, dumb power on stock heads the 317's will outflow everything else, but it will take 20psi of boost before you see any benefit. 243/799's are the best bet if you want to keep it NA with a stock head, but again, you need to see 7000+ on a 5.3 before you notice much of any advantage.
I had a set of 317's on a 421c.i. motor with 18 psi of boost and it ran very well once it was cranked up to 6500. The issue was that we rarely ran it over 6500 and the bottom end seemed sluggish (to me). I swapped on a set of 706's fresh from the boneyard with a quality one angle valve job. They increased the compression almost a full point with the 421 and the bottom end became just absolutely stupid with throttle response BEFORE the boost hit. At 14 psi it's a tire smoke machine before 50mph.
My point is that your 706's will out run your Gen 3 LM7 rods before you need to worry about a head upgrade for anything that you want to drive on the street. Let the LS advantages do their job.