They probably got it the same way I did, but using a different velocity.
The way it works is the bullet itself has a particular drag coefficient at any given Mach number. The G1 and G7 drag functions are given in tables of Mach number vs. drag coefficient for their respective reference projectiles. The BC in either system is just the number you multiply the reference projectile drag coefficient by to get your projectile's drag coefficient at the Mach number of interest. In this case, the standard atmosphere speed of sound is 1116.5 fps. The velocity I picked is 2700 fps.
2700 / 1116.5 = 2.418,
so I look for Mach 2.418 on both G1 and G7 tables. The ratio of the two will be the ratio of all BC's for the two drag functions at that one Mach number. The odds are 2.418 will actually fall between two Mach numbers on the table, and I interpolated, but the ratio in this instance was fairly constant over that range, and I could have used either of the bracketing Mach values.
The table of G1 and G7 drag functions near the Mach number of interest as cribbed from
the JBM site's Downloads area:
Mach 2.418's BC's interpolated from the above table are:
G1 = 0.5464 and G7 = 0.2742
The ratio of G7 to G1 is 0.2742/0.5464 = 0.5018
If we multiply 0.703 by 0.5018, we get 0.352786, which rounds up to 0.353. So that's what the JBM calculator is doing when I use Mach 2.418.
The 0.85% different 0.350 number in the Sniper's Hide thread is what you get when you use a velocity of 2830 to 2876 fps, or Mach 2.535 to Mach 2.576 in the ICAO standard atmosphere. That velocity is higher than Kilotanker's. With a 6.5-284, you might well be there, though.
So the question remains: What velocity was used to find the 0.703 number? If Barnes will oblige, then we'll get the more accurate G7 number, though I have to point out that a 0.85% disagreement is going to be smaller than the difference you can get from changing powders or even just among bullets in the same box.