As someone who has gone through this 3 times - for Allerton, More and White - if MF in Plymouth does not have a record of your generations in their files then you are in for a real paper-chase. MF Plymouth is a stickler for documentation with each couple needing to be identifed in some way as husband and wife and with each suceeding generation having the preceeding generation (parents) identified as being parents of that child in some way. Meaning there has to be a record, memorial stone or whatever that states who a child's parents are. One type of document that helped me considerably was having a number of 19th century family genealogies that were printed long ago in book form. This is acceptable although the Society considers family genealogies "weak" references but passable. And an effort should be made to try to retrieve all documents you can from applicable county clerks. These folks are often very helpful, I found.
But the first place to start is your state Mayflower society. These are the folks who will first process your application and they can be very helpful with advice too. I recommend you get to know them, especially their historian, as that person is the first person approving your application on its way to Plymouth.