I made up your circuit because I happened to have that chip lying around. :)
I typed in your code (can't include from an image) and tested.
The scope shows a frequency of around 7.6 Hz.
That would be confirmed by the screenshot of the logic analyzer. It takes 10.5 uS to send out one 16-bit value. That sounds about right as I reckon a single SPI byte to be about 3 uS, plus turning SS on and off. So that sounds OK, you can't do much better than that. Then another 5.5 uS for adding, and the loop etc. Total of 16 uS.
Now you are doing 4096 values up and 4096 values down to get one cycle. So 8192 * 16 uS = 131072 uS.
So your frequency is going to be 1 / 0.131072 which is 7.629 Hz, which exactly agrees with the observed frequency.
To speed it up? You could add more each time (eg. add 2 on the way up, subtract 2 on the way down).
But for remoting pots, well responding within 1/7th of a second is OK isn't it? But as I said, if you want faster, just add more each time. Of course, if you just want to jump from a setting of 500 to a setting of 1000 (with no intermediate steps) then that will take you 16 uS.