My last name is Skotak. In the documents I've found, I have seen: Skotak, Szkotak, Szkótak, and Skutak.
My family is Majda, but in America was translated , Maida, Meida,Maidan, Machda and even Makda, so to follow the family tree was a real mess.
I wanted to recover the nationality so I was trying to follow the family story with no success, I even werein the the small cities in Poland myself as a turist-reseacher but the lack of the language really makes a problem...
I am not sure if I can post email addresses my I got a guy that help me to build the family tree, he went to the the real state registries and confirmed names and match the story, so even if the birth certificate of my grand father was not existing, he created a new one. So maybe you should try them too. Their contact is email@example.com
Basically I show him some communication letters between the family and some photos, so he could guess the original city, then got a real state document of a land sold and there he got the real name, later he went to the local church and read in Russian the old documents... until they got the name of my grandfather as witness... this was the prove that the person really existed and thanks to that they created the new birth certificate needed to recover my polish nationality
I know that the story sounds crazy, but it worked... I spent too much time myself doing it alone that I was happy to find someone who could help me. I hope can help someone else too.