Nobody is taking perfect logicians as mere calculators. They can think/do anything they like, it’s just that nothing else is relevant to whether they leave or not, except the procedure which I have outlined. There are relevant consequences of there either being 100 blues or 99 blues (to each blue), but nothing else. Everything else, slapping included, is perfectly fine, but irrelevant to the exhaustive procedure of the correct solution.
This is enough to prove why no other solutions are valid in general.
Adequate specific disprovals have also been offered as a bonus, such as there being zero logical reason to choose to start counting from any particular number outside of the procedure of the correct solution. Further to this, there is no logical reason for all islanders to know which of the many combinations of e.g. 97 blue islanders are being referred to if they were to start counting from this or any other number.
No amount of knowing of knowing etc. can replace what the Guru says because none of this knowledge can be transferred, out of context, to situations where it no longer applies - such as the thought experiment of what 1 blue would do if there was only 1 blue (who would obviously only know what 1 blue would know and nothing more). It’s possible for each of 100 blue-eyed perfect logicians to attribute their knowledge to this sole blue, but inconsistent - and that is the problem. There is going to be a problem with any attempt at a solution that starts from irrelevance in order to “better” solve the problem (relevance as defined by the exhaustive analysis of the ONLY consequences that are to have any affect - as completely covered in the correct solution).
This problem has sufficiently been brought to a close.