Yes rock and bacterial populated live sand can be sources also but this was not included as these are not a "transmission" source, these are possible initial introductions.
Yes once a tank gets cyanobacteria it will come and go during the cycles throughout the year based on tank diversity.
My goal was to eliminate it permanently from a system unless reintroduced.
I have thought of Cyanobacteria as an opportunistic infection and not really "transmission" from a single source. When conditions are ripe, the Cyanobacteria dominate/explode in their numbers, i.e., when the tanks ecosystem is unbalanced somehow, the Cyanobacteria opportunistically take advantage. I think they are probably part of most saltwater tanks ecosystem albeit typically in small enough numbers to be non-problematic.
Although I imagine that it is possible that a single transmission can lead to an outbreak, it just doesn't seem to biologically make sense. I think Cyanobacteria are likely sharing our tanks with many other bacteria. I believe bacteria enter our tanks in countless ways. I imagine that Cyanobacteria are routine inhabitants in our tanks and are in a delicate balance with other bacteria and inhabitants. In terms of fish, corals and inverts being the source of a single transmission, most reefers are always fiddling with the tank and adding or changing their coral and fish regularly. So if a coral, invert or fish were the most routine direct transmission of Cyanobacteria, I might expect a wealth of reports when a new coral, fish and invertebrate was added and a resultant outbreak occurred. Except for your recent report of cross-contamination, I am unaware of seeing or reading of such reports. So I can certainly imagine cyano being associated with fish, coral and inverts, I just don't think that one new livestock addition as being the source for a cyano outbreak. In terms of what tips the balance in favor of cyanos over other bacteria and allowing for an outbreak, I don't know specifically. I think reasonable stable parameters and biological diversity of a healthy prospering tank likely keep cyano undetectable in the majority of tanks.
Eliminating a bacteria completely is a remarkable goal. I would think Cyanobacteria are likely endemic to saltwater tanks given their role in oxygenating our planet and their presence in the oceans as are likely a myriad of other bacterial inhabitants. It would seem cyano most likely are a constant player among the many bacteria out there. Biologically, I think expecting a 100% kill may simply not be possible given the many micro environments available in a reef tank. But clearly, whether 100% kill or not, hydrogen peroxide treatment certainly has been remarkable in effectuating a treatment for an acute cyano outbreak.