We traveled north through Salt Lake City in May (because of course it is on a direct route from Arizona to Wisconsin). During the winter I had acquired my grandmother's baptismal record through the efforts of a cousin in Poland, and I asked on the international floor if there was a Polish expert available. Maria was willing to help, and she began by searching several websites in Polish. We also rechecked for microfilm at the library without success. It looked as if I would have to be satisfied with just the names of my great grandparents.
However, Maria said, "I have a friend in Poland who might be willing to do research for you." She contacted him and he was able to seek records in both civil and church facilities. He ran into some of the same problems as we do here: he was not allowed to look at some of the civil records, and some of the priests were not willing to let him examine church records. He generally proposed that he would index their records in exchange for searching for a particular surname. He took photos of the records he was able to access and emailed them to Maria, who translated them for me.
As a result, I do have the names of my great great grandparents and four birth records, including my grandmother and three of her siblings! More proof that asking for help at the Family History Library is the best avenue to success.