Where can I find data on Mercury's orbit to fit a model to?
The available astrometric data for Mercury come from meridian transit timings (right ascension and declination) and radar or spacecraft ranging (distance).
NASA JPL has some
here,
and the French IMCCE has some
here.
To use those, you'll have to work out some geometry including the position of Earth in its own orbit.

For your purpose it may be easier to use numerical ephemerides via
JPL HORIZONS or SPICE,
or IMCCE Miriade or Multisat,
which can output Cartesian coordinates if requested.
Of course these are fit to observational data themselves.
The underlying data files (e.g. DE430, INPOP17a) come with papers detailing sources, methods, uncertainties, etc.