I'm still learning about house research, and I haven't had to deal with moved houses yet. Although I don't think any past deed would have to record the moving of a house, I would definitely still request copies of them all. Get all of the information you can. If the lot is sold a few times for a low price and described as a vacant lot, and then one year is sold at a much higher price and mentions the house, then obviously that will narrow down the time when it was put there, and you'll know who owned the land at the time. From there you could look up that person's previous address--maybe it was their own residence that they wanted to take with them.

When you write to the register of deeds, mention that the house was moved before 1947. If they see any other documents that has information on that, but isn't a property deed, they'll include a copy.

All I can think of is to try the Lincoln Park city government. Surely the taxes on the property went up when a house was put there. And they must have needed a permit to move the house, even in 1947. I have to believe that such a permit would mention its original location, but I've never had to ask a city clerk to look up such a permit before. If the city does not have any record like that, your next best course of action is narrowing down when the move happened and who owned it at that moment.

P.S. Did you have the State Historic Preservation Office send you a copy of the survey card? There is a tiny chance that it would have some information, or at least a photo from the 70s or 80s that you might find interesting.