Observations of SN 1987A by the Chandra High Energy Transmission Grating (HETG) in 1999 and the XMM-Newton Reflection Grating Spectrometer (RGS) in 2003 show very broad (v-b) lines with a full width at half-maximum (FWHM) of order 104 km s(-1); at these times the blast wave (BW) was primarily interacting with the H II region around the progenitor. Since then, the X-ray emission has been increasingly dominated by narrower components as the BW encounters dense equatorial ring (ER) material. Even so, continuing v-b emission is seen in the grating spectra suggesting that the interaction with H II region material is ongoing. Based on the deep HETG 2007 and 2011 data sets, and confirmed by RGS and other HETG observations, the v-b component has a width of 9300 +/- 2000 km s(-1) FWHM and contributes of order 20% of the current 0.5-2 keV flux. Guided by this result, SN 1987A's X-ray spectra are modeled as the weighted sum of the non-equilibrium-ionization emission from two simple one-dimensional hydrodynamic simulations; this "2 x 1D" model reproduces the observed radii, light curves, and spectra with a minimum of free parameters. The interaction with the H II region (rho(init) approximate to 130 amu cm(-3), +/- 15 degrees opening angle) produces the very broad emission lines and most of the 3-10 keV flux. Our ER hydrodynamics, admittedly a crude approximation to the multi-D reality, gives ER densities of similar to 10(4) amu cm-3, requires dense clumps (x5.5 density enhancement in similar to 30% of the volume), and predicts that the 0.5-2 keV flux will drop at a rate of similar to 17% per year once no new dense ER material is being shocked.