I have not yet tried this method yet...
However is seems red cyano can grow in an environment that has a high ratio of P to N, whereas cyano growth is limited by P alone. Low flow and light could play a role.
From my time in FW planted tanks, Blue-Green Algae grew in mats like cyano and was certainly known to be cause by poor water quality with high phosphates regardless of nitrate levels.
To the dismay of many reef keeper, in Fresh Water planted tanks this condition is remedied by sodium nitrate or potassium nitrate addition. SO with lack of a refugium (which I do have) P can be reduced by bacteria further with more nitrates when C is not limited.
Below is a link of N

:K manipulation that many successful planted tank owners have memorized. My suggestion is of course only valid if Red Cyano has many atribbutes of Blue Green Algae, which I believe it does.
So when I try this method after I get back from a planned vacation, I would guess Red Cyano could be control in the Vodka method by carefully creating P limited growth instead of N limited growth my carefully dosing NaNO3 or KNO3 to 3-5 ppm. I have no objection to using prodibio though.
I would suspect results would be seen in less than 4 weeks.
Here is the FW planted tank dosing strategy which I referred to. In those tanks, C is supplied as Co2 in 10ppm range to prevent limitation in plant growth. It may not work but is worth CAREFULLY trying.
http://www.thekrib.com/Plants/Fertilizer/sears-conlin.html