Such a mapping does exist in the dats, but our ability to extract it is incomplete. The dats include two icon IDs, one for the simpler old icons, and another for the new detailed icons. However, these icon IDs map to a list of internal icon composition instructions, which tells the game how to construct the final icon from the parts stored in the textures you have already found. These instructions are not just a simple list of texture IDs to composite, but also include position, size and color data. In order to automatically map spell/ability IDs to icons you will first need to figure out where that internal composition data is stored and how to read it (I suspect it's in a dat file somewhere, but I can't be certain). Then you can use the icon ID from the spell/ability dats to put two and two together.
Or, you could just use the icons we compiled manually for timers. Our icon set is mapped to the recast ID, so if you want it mapped to spell/ability ID you will need to do a little bit more work, but that's easier than redoing all of the other stuff.