Thank you, Robert!
Using gp.clip_management works much faster indeed and also produces jpgs. The only thing that bothered me was that the clipped image was not of the same brightness as the original. Now I added the line: gp.compression= "LZ77" and everything looks awesome!! Thank you again, Robert!
Attached is the working script.
As I cheched again the pixel values of the result are not the same as the original's, despite the LZ77 setting.. Any thoughts on how to achieve that the pixel values of the clipped image remain the same?