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Help with the orbit coordinate system

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I'm working on yet another landing guidance plugin. I'm almost ready to share an early version, but I'm having trouble with the coordinate system. In particular, I'm trying to find the latitude and longitude of the active vessel on its current orbit at some arbitrary time in the future, taking into account the rotation of the planet.

The code looks something like this (with a nod to KER for inspiration): 

Vector3d position = vessel.GetOrbit().getPositionAtUT(currentTime + deltaT);

double bodyRot = 360 * (deltaT) / body.rotationPeriod;
double lat = body.GetLatitude(position);
double lon = NormAngle(body.GetLongitude(position) - bodyRot); //NormAngle normalises the angle between -180, 180.

When I continue on the current orbit and sample the actual lat and long at UT = currentTime + deltaT, I find:

a ) Lat and long are both a bit off (0-2 degrees), thought long is usually more wrong than lat (possibly suggesting that my bodyRot is incorrect).

b ) The error is greater the further in advance I try to calculate the lat and long (if I calculate no more than a few minutes into the future the error is negligible).

I suspect that my understanding of the value returned by Orbit.getPositionAtUT() might be incorrect. It seems to return a value which is sort of "the position that the vessel would be in at time UT if the main body stopped moving", which I think would make my logic consistent. But either of those assumptions may be wrong.

Can anyone offer any advice, or an alternative method?

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