apophenia.... you write:
So yes, I would agree. A maximally great being is incoherent.
Here, your prejudice against the argument is the cause of this conclusion...
The unprejudiced conclusion must be that a qualitative great being is coherent.
The Anselm Ontological Argument has been computer simulated with the result that it is valid (perhaps, not necessarily sound but valid non the less).
One can even compare the argument to the existence of the "Perfect Chess Game" (this example directly deals with your positive & negative property idea)... and indeed the Perfect Chess Game does in fact qualitatively exist... so this too is coherent.
Clearly, the quantitative is different... with regards to the Perfect Chess Game being quantified we get drawn into the N=NP mathematical problem...
However, bottom line... if one is not prejudiced then the body of evidence points to the fact that Ontological Argument is valid, i.e. coherent.
What is interesting apophenia is the method of criticising the Ontological Argument you use, i.e. delimiting Reason... this I find interesting.