got your mail and yes, I did find a connection between Jasinski and Burzynski in the area of Panigrodz but that does not nessesarily mean that these are your people. I do not actually look our for this connection and I have already found the Burzynski I was looking for but if I can I will try to help you.
I had a look at the censuses of Milwaukee and this that I found your people. Have you got all this censuses?
I also found your people in the immigration records and I do have the passenger records. It is just a shame that this records do not show a "last residence" at all, so they would not help very much they just give you the date of immigration. Found the once for John Jasinski and his parents as well as Katharina Burzynski and her parents and family. If you like I can sent the immages to you. Just tell me.
What I could not find is Josef Zielinskis passenger record. I have seen him in the 1900 census living with his daughter Antonina Orlowski (agewise she can only be his daughter-not his sister) and her husband next to John and Katharina Jasinski. Its funny that the 1900 census shows him as immigrating in 1886 while Antonina and her husband only immigrated in 1888. Maybe the figure is wrong but if not that could lead to something. It could mean that he came with his wife and other children. Thinking that he was already 56 when he immigrated could indicate that he did not just come alone or just only with his wife. So the first things you should do it gathering all material you can find in Milwaukee - like the death records of the parents and also have a look at the birth records of the children and look at the godparents. Vey often they were related.
I am living in Germany and here I order the films from the family history center to look at the church records of parishes in the poznan area. I have also joined the poznan marriage project which tries to collect marriages in the poznan area from 1830 to 1880. Well your family is still not in it but one has to watch out.
As for your people I also had a look at the world war I records - but shame, they also do not give any birthplace at all.
Just do not give up start with everything you can get in Milwaukee. Try St. Adalbert and get the burial records.
Just tell me if you like to have the passenger records I found.