I am trying to map an irregularly gridded dataset (raw satellite data) with associated latitudes and longitudes to a regularly gridded set of latitudes and longitudes given by <
More than likely, griddata is way too hard. It's designed to work with randomly sampled data. Your data is almost certainly regularly sampled -- just not on the same grid as your target output grid.
Look at a much simpler approach like an affine transformation or a series of affine transformations on small chips if the earth's topology or curvature affect yoru results.
There are some out of the box solutions that might help. GDAL is a good example.
Also, this type of issue is often discussed in GIS. See:
https://gis.stackexchange.com/questions/10430/changing-image-projection-using-python