The distance represented by one second west of a known point will be more for you than it is for me because the lines are closer together here.
What I would do is go out to that one pivot you know the coordinates for and measure off 31.25' due west of it and see what the exact coordinates are for that point. The difference will be the number you have to add to each long. number. As you get more than a couple miles north or south, you may want to check another pivot to see how much it will vary with a change in lat. If you know that difference, you should be able to interpolate for other pivots if it is significant. Granted, the differences will not be exactly linear but at you latitude, I'd guess it will be insignificant.