Namaste Nidhi,
Where is the frieze in your post located?  Can you post a larger copy of the image?  I'd really like to see the depiction of that katar in detail...
I have Coorgi friends and my wife's family is coastal Kannada... I've been on the lookout for a nice ayudha katti for almost 13 years, and always make time to take up the search when we're back in India... 

 I'll also be on the hunt for a good pichangatti on my next trip. 
Anyway, to your knowledge, has anyone ever published anything on when the southern kukri evolved into the ayudha katti?  Unlike the visible "kukri kink" I found in the 12th C. friezes in Halebidu, the 15th C. example you post seems to more closely resemble the ayudha katti in form...  
Thank you for posting that - before coming across these friezes a couple years ago, I had always assumed the ayudha katti to have been a (later) southern adaptation of a northern weapon, and had no idea the Indian kukri in its classical form had preceded it in the kingdoms of the south.