XY Coordinates for Points in odd format, not matching any projection

Question

I am trying to match up some data without success. I have a state shapefile from the TIGER/Line and a series of X/Y Coordinates from a St. Louis, Missouri police department (CSV).

I am using an OpenStreetMap basemap in QGIS 2.14.8 to verify the data is in the right place.

The Tiger/line shapefile is in NAD83.

The XY coordinates are in what I can only guess is U.S. Survey feet? Example: "903948.39, 1033477.17". I do not know what CRS they are in. When I try to project them to..well..anything, they do not match up to the Tiger/line shapefile. I assume this is because the units are so wonky.

Is it possible to display these points in a format that will actually coincide with the Tiger/line shapefile? I'm not sure how to convert them since the units are wonky. Simply changing the projection to NAD83 does not help.

If it is possible, will this solve the problem and how do I do it?

Answer 1

Edit: Nevermind, I found the answer.

I mistakenly thought (1) that you needed to have base map and the XY coordinates in the same projection and (2) needed to have them stored in the same distance units. This isn't the case..I'm still quite new to GIS.

I fixed the solution simply by looking up the different State Plane Coordinate Systems for Missouri and going through the list, trying the ones that made the most sense from where I knew the data to be from.