This was all done in ArcObjects Java, but you can apply the process to your language.
We created a buffer polygon by buffering the subject parcel by 300'.
We create a spatialFilter setting the geometry to the buffer polygon
Then we get a featureCursor of all parcels that intersect that buffer polygon by applying the spatial filter to the featurelayer's searchDisplayFeatures method. We get a featureCursor for opposed, a featureCursor for support and a featureCursor for no response parcels.
We loop through each featureCursor and get the geometry of each parcel in the buffer and then intersect that feature geometry with the buffer polygon and store the resulting geometry in a temporary geometry object - which then gives us the area of the intersecting feature.
I believe the Polygon class has an intersect method that we used.
Let me know if I can answer anything more...