I think it is important to remember that most of the historical records we use for genealogy today were created for other purposes (not for genealogy). To find records, we have to understand why and how they were created. For civil records, that often means that some law was passed mandating that the records should be collected; those laws will say what information should be collected and what form it should take. For church records, the records kept would depend on what the church's own hierarchy required.
So -- to discover what records might have been created in a particular time in place, search the civil codes to see what laws were in effect at the time. Kimberly Powell's article on About.com, Historical U.S. Statutes Online, is a good place to start.
See also the related question How can I determine what records are available in a particular locale?
If you cannot find specific records that outline the members of a household in detail, then you have to do the next best thing by seeking out records which are more likely to contain the names of groups of people, like probate records or newspaper articles that talk about family events and list the names of multiple people (obituaries, funeral notices, articles about weddings or anniversary parties, and the like). For tips on how to pull all the bits and pieces together, the FamilySearch Online course by Dr. Tom Jones on Inferential Genealogy might help. Another way to find more records might be to look at articles about what records people use to substitute for the 1890 US Census, which was destroyed by fire.
Resources for Pennsylvania:
Resources for New York State:
The remainder of this answer addresses content that has subsequently been edited out of the original question. I'm leaving it in place to help other researchers.
If you can't move backwards through the generations, that's a sign that you haven't learned enough about the generation where you are stuck. Do a broader exploration of the later time before you attempt to move back in time.
In many cases (later than the period you are working on now) I was unable to find records with direct information about the parents of the person I was seeking, but I was able to infer the parents' names by examining all the information I had about the entire group of siblings.
- Study the friends, associates, and neighbors ('cluster' or FAN club)
Another way to gather more information is to deepen your understanding of what you find by studying the subjects related to your questions. To use your example, you might look for other case studies about people from New York state who moved to Michigan, or articles about migration patterns for people who moved from New York to Michigan. Seeing what other genealogists have done provides knowledge about local records that you may not know about.
- Study the record groups for the records you've collected already
Have you gotten the most out of the records you already have? How complete is the entire record group? What records exist which are not online yet? What pointers to other records are in the records you have? Have you followed the pointers from finding aids back to the original records?
- Study the geographical areas involved
In some cases, the best way to solve these questions about whether your person left location A and moved to location B can be solved by means of a one-place study of both locations.
For one of the lines I've studied, I discovered that there is a doctoral dissertation written about the immigrant community in the town I am researching. Reading a work like that, even if it doesn't contain the name of any of the specific individuals I am looking for, gives a wealth of information about the entire community. Small details in historical records which seemed insignificant when I collected the records suddenly take on new meaning, and become pointers to other records.