[werk_ag]

It seems clear that you may need to reduce the sensibility of the system even a little more.
I think you can't expect that the readings will be coincident to theoretical graph or that they start exactly at sunrise time, some time before that, already there are enough radiation (IR + visible light) on the sky for the sensor to start to read.

I'm somewhat surprised by the frequent use of the expression "Frustrated"...
Sorry, I wonder if you have read what is said on the topic where the Solar /UV interface is announced:

"Please bear in mind that to a successful build of this sensor, you may need to spend a considerable amount of time and effort.
With the Solar / UV interface you can build a reasonable solar radiation sensor, but don't expect that this task will be just a matter of connecting the parts and that's all. You may need to spend a considerable amount of time and effort to calibrate it.
For installing it in a suitable case, you will also need a lot of ability and imagination.
If you are not sure about what you're doing, PLEASE, don't order this device. "