"Organic " is a pretty slippery term. In chemistry it mostly means compounds that contain carbon, but there are some simple carbon compounds that are not considered organic.
In agriculture, it's even more slippery. Most organic fertilizers are derived from living (or once-living) organisms, but not all. Most fertilizers that are approved for organic use do have the plant-essential elements bound up in carbon compounds, but not all (e.g., potassium sulfate, sul-po-mag). Pretty much it comes down to a list of what's approved by an organic certification body. What they are after is materials and methods that promote healthy ecologies, sustainability, promoting the use of "naturally" derived materials and avoiding the use of "synthetic" materials. The exact same material from a natural source can be approved, while the same material from a synthetic source is prohibited (e.g., urea).
It is true that the essential elements are taken up by the plants in the same ionic (not salt) forms, regardless of source. It is also true that fertilizers where the essential elements are bound up in carbon compounds require microbial activity to break down the compounds and release the essential elements so that they become available to the plant, so these are slow-release. This prevents the essential elements from being leached, so flushing is much less effective for these kinds of fertilizers than for synthetic ferts that supply essential elements in forms that are readily available to the plant. However, in media with high cation exchange capacity, synthetically derived cations (K, Ca, Mg, etc.) will not leach either.
We are mostly looking to leach out N, available to the plants as NO3- (nitrate) and NH4+ (ammonium), and often supplied as organic or synthetic urea. Urea is water soluble, and is nuetral but polar. So media with high CEC tends to retain N in ammonium and urea forms.
What any of that has to do with how well Advanced Nutrients Connoisseur works, I am not sure, but the original poster was looking for suggestions or rants.

penguin