Here's all I know so far. My ggf was born in Pisek, CZR. He, all his siblings and mother came to the USA after their father John Kloboucnik died. His wife remarried and had 2 daughters here.
I went to Praha several years back and hooked up with a Karel Kloboucnik. He and his parents lived in Plzen. His father looked just like my father. I had a picture of my ggf. They said it looked like their uncle in Pisek. I figured that we were closely related, since at the time I didn't have any of my ggf's siblings or parents names. It probably goes back one or two generations further though. Possibly my gggf's brother is who they descend from. Since Pisek seems to be the place of their family and mine, it may also be yours.
Since this part of the world was Bohemia, Austria, prior to 1900, your "Austrian" line probably came from there also. If the Czech archives come online soon we should be better able to find them. I have heard the LDS is working on theses records, or at least has finally gotten the okay to digitize these. Otherwise a trip to Praha might be in order. I would be lost since I know no Czech. You can email me at email@example.com
if you wish. My grandfather shortened our name from Kloboucnik to Klob after he graduated from dental school. I have quite a lot of info on my Kloboucniks, here in the USA, who largely settled in Chicago