JOHN,
You haven't provided much information on which to base an analysis of your puzzle but I can suggest two possible answers.
The first is speed related. Aerodynamic damping varies with speed so if the experiments were conducted at different speeds this might cause the spiral stability to change from being unstable to stable.
My second suggestion is C of G related, and is based upon the (possible) clue that the aircraft became stable in the final test. Aft movement of the C of G reduces longitudinal and directional stability but has little if any effect on lateral. If in the first two tests the C of G was sufficiently forward to give strong directional stability, this might produce the spiral instability effect you observed. If by the time of the third test, the burning of fuel had moved the C of G far enough aft, it might have been enough to make the aircraft spirally stable.
BOOKWORM
The main area of our disagreement appears to relate to whether or not an aircraft exhibiting Dutch role can be spirally stable. In my first post I did not actually say that an aircraft must be spirally unstable. What I actually said was that if it rolled away from a sideslip more than it yawed into it then it would exhibit Dutch roll. And if it yawed into a sideslip more than it rolled away from it then it would be spirally unstable. I must confess however that in my second post I made the mistake of disagreeing with your statement that " the tendency to Dutch roll does not necessarily imply a positive stability in the spiral mode, or vice versa." I think this is case of "you should have read what I actually said in my first post and what I meant to say in my second".
Perhaps we can agree on the following:
If lateral static stability is stronger than directional static stability the dominate mode is likely to be Dutch roll. This might however be accompanied by weaker spirally stable or unstable motion. If directional static stability is stronger than lateral static stability, then the dominant mode is likely to be spiral instability. This might however be accompanied by a weaker Dutch roll.
GENGHIS
I did not suggest that your arguments were too long, but rather that they were perhaps aimed too high. This suggestion is based upon an assessment of SHOCKWAVES profile and the type of questions he has asked. These led me to conclude that he has probably gained his ATPL quite recently and is now attempting to master the technicalities of his first commercial aircraft. In view of this assessment, I based my first post on the level of knowledge that he would have required to pass his ATPL exams. My post was intended to assist him in applying his existing knowledge to solve the problem for himself. If my assessment was correct, then your references to partial derivatives would have added little to his understanding. He could of course have done a Phd in aerodynamics and just be testing (and probably laughing at) us all.
JOHN, BOOKWORM AND GENGHIS
Now what about SHOCKWAVE'S second question?