There's little similarity between prewar Poland and 21st century America, imho.
Marianna was definitely uncommon in the 1930s so if someone didn't want to stand out, they would have chosen Maria ... but since you're lucky enough to know enough Poles and Polish Jews in the US to support your every -even least probable -claim, on every topic, who am I to argue with it.
Back on topic. There's one more thing to look for in old records (apart from wyznanie mojzeszowe), the word 'starozakonny' (starozakonni etc), which is an old fashioned way of referring to Jewish people (literally 'of the old order').
Here's how it's used:
And the site where I found it, which might be of some use for you
Certain advice included there concerning looking for birth records would be sort of universal for different religions.
And as far as I am concerned, if you really want to find out the truth, it's high time to invest some time and money in professional help. Start with looking for the birth records of the last of your ancestors who was born in Poland, then their parents and so on.
It's hard to say if you succeed in finding what you're looking for, but it'll definitely be more probable than a random internet search.
Some other examples of Jewish records:
The birth record of Szmul Tuchmic from 1923 - it includes information about wyznanie mojzeszowe
Another site in Polish with different examples of birth and death records of Polish Jews from the early 19th century -scroll down for photos. These include the word starozakonny.
Of course, things might have varied depending on the parish but to be sure you need some solid information from the state archives. Contact them. Even if you don't have enough money to do everything at once, do it step by step.