Stars are so massive compared to planets, a moon won't move the null field point much, really. The easiest way to simplify a problem like that is to find the center of mass of the planet-moon system, and use that as the starting point with the star. For the earth-moon system, the center of mass is inside the earth. If you assume the earth-moon relationship is "normal", you're going to be out of luck for most planet-moon pirate points.
You are not looking for the center of mass, you are looking for a point where the gravity of two objects cancels out. Note that that the center of mass between the Earth and the Sun is about 280 miles from the center of the Sun, yet the Earth-Sun L1 point is ~1,500,000 km from Earth.
(Center of mass is proportional to the distance between two objects, while gravity strength is inversely proportional to the square of the distance between two objects. Very different)
As for the calculations, I'd expect a Jumpship or Dropship's computer can run the calculations to figure out the pirate point. You have semi-live coverage of the system, you know where the planet is, and you can look up in records if the planet has a moon. If not sure, you just pop to the planet-sun jump point. Depending on time delay between destination and observation (i.e. if 10 light-minutes away), you can just have the computer move the bodies forward by half an hour, and plot the Pirate Point coordinates based on that data. Assuming you can do the math in less than 20 minutes, you will get the Pirate Point coordinates, and can pop to the destination easily. After arriving, it is the helm officer's job to park the Jumpship in a halo orbit around the L1 point (and out of the jump limit).
Who knows, the Star League probably had something where you plugged in the mass of the star, distance to the star, the target planet's current orbital distance, the target planet's nearest/largest moon, angles between them, and it would provide the relative coordinates for the navigator to use taking into account all the math. Unfortunately, that computer program was lost with the fall of the Star League.