There are three things to keep in mind here:
1. It really doesn't matter which point is used as the Dead Reckoning Position. You can try to use for this each of the 4 vertices of the square, inside which your actual position is located, and performing the LOP transfer in all four cases you will get practically the same observed position.
2. It is not necessary to use coordinates rounded to the nearest degree as Dead Reckoning Position. It makes sense to take DRP into account to within minutes of arc.
3. The closer the Dead Reckoning Position is to your actual position, the more accurately you will determine your actual position using celestial navigation. In this case, the actual curvature of the LOP (which we depict as a straight line, even though it is a large arc) will not have a noticeable effect on the result.
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