How many Endogenous Retroviruses do we share with other primates?
There are several papers that cover this. Briefly, humans share the vast majority of their ERVs with other primates, but not all; and this is mainly because other primates have acquired ERVs that humans have not (rather than humans acquiring new ERVs themselves).  The third link, in particular, seems to cover your proposed reconstruction and concluded that in general "these sequences gave trees that were consistent with the well established phylogeny of the old world primates".


Divergent Patterns of Recent Retroviral Integrations in the Human and Chimpanzee Genomes: Probable Transmissions between Other Primates and Chimpanzees
The decline of human endogenous retroviruses: extinction and survival
Constructing primate phylogenies from ancient retrovirus sequences