I managed to solve both problems.
I got rid of the bouncyness by reseting the objects when the grab is removed:
Code:
else:
if grab != False:
grab.getDst().reset()
grab.remove()
grab = False
I got the objects being recognized by not removing the DropBin bounding boxes but rather make them invisible (and I also remove the objects from the scene as soon as they are inside of a bin)