Since you are still struggling with this, it might be an idea to take into consideration the differences between the old style scandoublers and the Indivision.
It is my understanding that old scandoublers did nothing more than double the output frequency from the Amiga, something which worked fine on crt monitors. Modern lcd monitors on the other hand, are more problematic since they are a bit more picky regarding the frequency. As a result of this, I belive the Indidvision is made to output a little more than just the double of the Amigas frequency, this in order to make it more compatible with modern monitors.
My theory is that the reason for your problems might be because the Picasso II pass-through expects a signal with the same frequency as old style scandoublers. But have in mind that this is just a theory I have, for I'm no expert on this matter.