As part of our program to map the large-scale distribution of galaxies behind the Milky Way, we used the Parkes 210 ft (64 m) radio telescope for pointed HI observations of a sample of low surface-brightness (due to heavy obscuration) spiral galaxies selected from the deep optical Zone of Avoidance (ZOA) galaxy catalog in the Hydra/Antlia region (Kraan-Korteweg 2000a). Searching a simultaneous velocity range of either 300 to 5500 km/s or 300 to 10500 km/s to an rms level of typically 2 - 4 mJy resulted in detections in 61 of the 139 pointings, leading to a total of 66 detections (an additional detection was made in a reference position, and two other pointings revealed two and four independent signals respectively). Except for 2 strong HI emitters identified in the shallow Zone of Avoidance HI survey (Henning et al. 2000), all HI detections are new. An analysis of the properties of the observed and detected galaxies prove that pointed HI observations of highly obscured galaxies allow the tracing of a population of nearby, intrinsically large and bright spiral galaxies that otherwise would not be recovered. The new data identified a previously unrecognized nearby group at l=287.5, b=-9.5, V=1700 km/s, the continuation of the Hydra/Antlia filament on the opposite side of the Galactic plane, and helped to delimit a distinct void in the ZOA centered at 2000 km/s.