Calculate NEO object position with nasa Near Earth Object data
The file you had linked as 'Detailed NEO Data' lists all the orbital parameters needed to determine the position of the object as a function of time. It lists these parameters for the objects orbiting the earth. This should be just what you need. They are located at bottom of file. There are routines to convert the orbit in orbital parameters to cartesian coordinates. This may be easier to use. You can google on orbital parameters conversion to find these routines. I think I have a copy in Fortran but not many people use Fortran now.