Some examples of the resolution loss you are experiencing would help.
I can tell you that some time ago I did some exercises in transforming an image into some crazy shapes (spheres, waves, spiral) and found that upsampling previously the image in Photoshop to a size N times larger than the ouput size, allowed me to do these transformations using a hyper-basic nearest neighbour transformation (the only one my programming skills can afford), and still get a very high quality output.
Some examples here. As expected, straight nearest neighbour produced aliasing and information loss, but resampling the images prior to the basic transformation radically improved the result.
left: input image,
centre: straight nearest neigbour transform,
right: upsizing + nearest neighbour transform + downsizing.
SPHERE MAPPINGWAVE MAPPINGSPIRAL MAPPINGMaybe if you previously upsize your scans, then apply the transform, and finally downsize to the final format can improve your results.
Result