Hello, please accept my apologies for the delay in my reply to your message.
I may have indicated before that I am in possession of very detailed materials collected and published by Dr. Erwin Jaeckle (Switzerland) who is also one of my relatives. And possible yours, of course.
He was the most knowledgeable family historian. Based on his material and my own research I have made an unfinished family tree of my branch of the family (male line only, since it was tentative.) Never finished.
This tree is posted on ancestry.com.
If you do not have the Erwin Jaeckle materials, I could make a copy available to you. There is also a small booklet that was written by one of our other relatives. I have that one as well.
With a little more effort and energy someone could easily research the root of the family beyond 1430. I know what German archives may have additional materials. By the way, it is very rare that any family records older than about 1630 are available.
In our case, most of the records were destroyed when the monastery of Sankt Georgen burned down.
The family originates not from Schwenningen directly but from a small hamlet close to it. There the oldest recorded Jaeckle (Jaecklin) held the "Koenigslehen" as a fief from the monastery of Sankt Georgen.
Please let me know if you want to have some more info.
PS: What do you think when you hear that one of the ancestors was beheaded? A woman!