I run about 40 seconds every 15 minutes, so I run just about the same as you except mines the KA-4.
Do you have your baro set with a manometer? If you have too much draft it could cause the fire to burn too hot when you're at idle.
Based on the size of the fire at idle for 1/2 a day, I think I can get it down to 30 seconds every 15 minutes with no problem. I may try it soon as we are seeing some days ~50F outside.
Over the summer I will see "How low can I go?"
Also, do you have the little auxillary fan running? I do not, I may have to hook it up for summer use though. That may allow you to reduce your timer some more.
Keep us posted.