What can we do to find the "link"?
There are lots of Zychas in Austria, a few in Germany, and apparently quite a few in Poland.
And apparently they are all related.
The furthest back I have found (with very little effort on my part) was Adolf Zycha, who was Dean of Bonn University until 1933. If I knew around what time your Zychas were born (or just alive would be a start, as I don't know many births of Zychas; I'll find out though.