Bryan Litz's book, Ballistic Performance of Rifle Bullets lists measured BC's to use. Manufacturer G1 box numbers are often given at the high end of the velocity range they expect the bullet to be used at for competitive selling point reasons. These numbers work OK to 300 yards or so, but will mess up with long-range calculations. For the 147-grain ELD from Below 3000 to below 1500 fps, the measured G1 BC drops by 16%. The G7 BC only drops about 6% in that range and would be better to use.
However, you don't have to rely on a BC model to approximate Hornady bullet performance anymore as the Hornady 4 DOF calculator is linked to a list of actual Doppler RADAR-measured individual drag functions for its bullets. In very long-range shooting, where BC errors accumulate by the time the bullet gets to the target, this will always be the more accurate way to go, try the advanced calculator.
I ran it for your altitude (average barometric pressure 28.70 in-Hg at 1200 feet) in 80°F and with 50% RH, where Mach 1 works out to 1,142.5 fps
according to this calculator. (Humidity thins air density, but is not a huge influence; going to 78% RH raises Mach 1 to 144.3 fps). What the Hornady calculator shows is the bullet needs to start out with a muzzle velocity of 3155 fps to fall just to that speed of sound at 1760 yards.
I looked further to see what would happen with range calculations from BC's to see how far off they could get, and the answer is, a lot. For each BC type (single G1, single G7, multiple breakpoint G1 and G7 tables) and for the single BC numbers I got disagreements of over 200 ft/s between various ballistics calculators. The reasons are cumulative iteration and rounding errors and conversion precision errors between native metric and native inch calculators. When I went from the BC on the box through the measured G1 and G7 average BC's as well as the multiple BC's broken up by velocity ranges, the result showed required muzzle velocities from 2756 fps to 3064 fps to stay above the speed of sound to 1760 yards. All were slower than the actual drag function says is required because what is actually required is greater for an important reason:
As you probably know, drag coefficients rise sharply at the speed of sound and change a lot with relatively small changes in shape. This matters because it means BC-based calculations can be easily befuddled in what is called the transonic velocity range. Why? Well, bullets have curves and angles on their surfaces and the air flows over them all at once. When the bullet is going at exactly Mach 1, the shockwave formation drops off, but air flowing over the ogive has a greater distance to travel than air along the sides does with the same amount of distance covered, so there is some supersonic airflow over the ogive at Mach 1. The tail also should have that, but laminar separation can occur, and at what velocity and bullet diameter that occurs depends on the angle of the boattail. The net result is there is changing drag messing with the bullet starting between about Mach 1.2 and 1.25, depending on the bullet profile. It doesn't stop completely until below about Mach 0.75 and 0.85, again, depending on the bullet profile. So the transonic range can be considered anything from Mach 0.85-1.2 to Mach 0.75-1.25, and some bullets can get jiggy in that range. So, if you want the best ballistic performance, you really would prefer to keep the bullet from falling into that transonic range, though some will get through it a lot better than others.
Quite a mess, isn't it? Bottom line, I think you'll probably like the .338.