I've never considered the Llano to be the hill country - it drains the high mesa - though it is good kayak water.
To me, the hill country is the limestone spring creeks that emerge from the escarpment roughly along a line from Rock Springs to Harper.
From 40 years of doing this, in wet years, the farther west you go, the better you find, but any of these headwaters will fish clear water 48 hours after a flash flood.
This is the Pedernales headwaters 48 hours after 900 cfs blew through this little creek.
This is the Guadalupe above Center Point running 250 cfs. I caught 200 bass this day fishing only the chutes with a sinking line.
If you want a kayak recommendation and don't mind pay camping, visit Chalk Bluff Park on the Nueces, west of Uvalde, and float in from above.