You've probably long since moved on, but, just for reference, the initial conditions HORIZONS uses are mentioned ("header.431_572") in ftp://ssd.jpl.nasa.gov/pub/eph/planets/Linux/README.txt but the only place I could find them in "table form" is in my own git repository:
https://github.com/barrycarter/bcapps/blob/master/ASTRO/header.431_572
The values are explained in http://ilrs.gsfc.nasa.gov/docs/2014/196C.pdf starting on page 39, "VI. Initial Conditions and Constants", especially in the tables starting with Table 4 on page 47 and ending with Table 13 on page 74.
I've written scripts to setup the initial conditions and numerically solve the differential equations using Mathematica, so the following may be helpful:
https://github.com/barrycarter/bcapps/blob/master/ASTRO/README
https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-header-values.pl
https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-integrate.m
The output of the Perl script above, which includes all the equations you'll need, is: https://github.com/barrycarter/bcapps/tree/master/ASTRO/bc-integrate-init.m
When I reduce the step size sufficiently (Mathematica's default step size is too large), my results closely match those of HORIZONS:
https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-integrate-compare.m
