This work extends our earlier investigation of the near-infrared absorption spectroscopy of atomic bromine (Br) trapped in solid parahydrogen (pH2) and orthodeuterium (oD2) [S. C. Kettwich, L. O. Paulson, P. L. Raston, and D. T. Anderson, J. Phys. Chem. A 112, 11153 (2008)]. We report new spectroscopic observations on a series of double transitions involving excitation of the weak Br-atom spin-orbit (SO) transition ((2)P(1/2) ← (2)P(3/2)) in concert with phonon, rotational, vibrational, and rovibrational excitation of the solid molecular hydrogen host. Further, we utilize the rapid vapor deposition technique to produce pH2 crystals with a non-equilibrium mixture of face centered cubic (fcc) and hexagonal closed packed (hcp) crystal domains in the freshly deposited solid. Gentle annealing (T = 4.3 K) of the pH2 sample irreversibly converts the higher energy fcc crystal domains to the slightly more stable hcp structure. We follow the extent of this conversion process using the intensity of the U1(0) transition of solid pH2 and correlate crystal structure changes with changes in the integrated intensity of Br-atom absorption features. Annealing the pH2 solid causes the integrated intensity of the zero-phonon Br SO transition to increase approximately 45% to a value that is 8 times larger than the gas phase value. We show that the magnitude of the increase is strongly correlated to the fraction of hcp crystal domains within the solid. Theoretical calculations presented in Paper II show that these intensity differences are caused by the different symmetries of single substitution sites for these two crystal structures. For fully annealed Br-atom doped pH2 solids, where the crystal structure is nearly pure hcp, the Br-atom SO transition sharpens considerably and shows evidence for resolved hyperfine structure.