Basically, any speculation that is not backed up with firm documentation remains vain speculation. And without firm evidence to the contrary, there is no good reason to suppose that your family was originally Jewish or Gypsy rather than ethnically Polish. Piątek is a rather common Polish surname.
Records become scarcer as you go back in time, and, in Poland, many did not survive the wars and the ravages of time. Paper is rather perishable even under the best of circumstances. For many, if not most people from 19th century Poland, the only records that would have been kept are church and civil records of birth, baptism, marriage and death, and of military service, tax assessment or land transactions if you are lucky. No documentation remains at all of many, if not most people from 1800 or earlier. It's not at all surprising that your paper trail ends in the mid to late 19th century.
Also, most Poles did not use surnames until about the time of the partitions, and even then, some families didn't until the early 19th century, and sometimes later, until they were imposed on them by the authorities.
This is even more true of ethnic minorities, not only Jews and Gypsies, but also of Ruthenian mountaineers who lived in the "very south of Poland, almost to Slovakia".
While it's conceivable that the name Piątek was given to or adopted by Jewish converts, it is also a name commonly used by ethnic Poles, and probably a lot more so than by Jews. Like I said, there is no particular reason to speculate on possible Jewish origins in the absence of compelling documentation to the contrary, which very likely may no longer exist, especially for the area you describe, which was forcibly depopulated after WWII. Many of the churches where records may have been kept were abandoned to decay, records and all.
My grandfather's last name is Piatek, which from what I understand simply means "Friday". Is that a pretty common last name?
PIĄTEK: Friday, the day someone was born or maybe converted to Christianity. Quite common in Poland with some 19,000 users.