Not all pixels are being mapped to because you only Pxl-On if there was a Pxl-Test.  This restricts sprites to have the same number of pixels in the best case even though there could be a lot more when the sprite is rotated and I'm not even including the overlapped pixels.  Instead what you have to do is get a bounding box of the destination zone (which could be the whole screen) and then run for loops over the region to see if each destination pixel belonged to the original image.  So you need to find the inverse in your eqaution first of all:

X_I = ([X - X_Offset] * cos a) + ([Y - Y_Offset] * sin a)
Y_I = ([Y - Y_Offset] * cos a) - ([X - X_Offset] * sin a)

Something like that...  So you for loop over the X and Y bounding box, pixel test if (X_I,Y_I) is shaded, and if it is, fill in (X,Y)