I'm along way from finishing, but on the basis of the grid I have so far I can tell you that the co-ordinates conform to maths practice. So AN, for example tells you that the answer starts in column A, row N. What makes it tricky is that the co-ordinates do not uniquely identify cells since there appears to be more than one column A, for example.
If you look at the down clues it's possible to work out which must start in the top row. In a 12x12 there must be at least eight entries starting in the top row to avoid consecutive unchecked letters or otherwise non-Ximenean checking. If you solve all or most of those and write them in aligned vertical columns in any order, you may see that in one row you'll have all the letters of the AI across answer, which is a straightforward anagram.
While there is still lots to puzzle me I am sure my approach is right because my half-formed grid has enabled me to get the first clued across answer, the wordplay to which is very obscure. I would never have solved it cold.