Hi Steve,
I am facing with the same problem now, and I found Dean's question and your response. I am wondering have you figured out why the re-sampling is happening? I have tried to re-sample my input raster to much smaller cell size then extract by mask to the new input raster, but the cell values are still different in the output raster, even the very center cells. I have set up the extent of extract by mask to be the same as the new input raster, and chose nearest as re-sample method. To my understanding, it should at most only change values of the cells at the edge?