Knocking out HIV DNA was demonstrated in 2014. The complete excision of HIV from the genome as the PNAS paper describes is a possible method, however, there are other options. The method proposed here is to target the reverse transcriptase gene of HIV as well.
The ability of CRISPR to delete the HIV genome in cell culture is excellent. By pairing it with a second CRISPR system that destroys the viability of the reverse transcriptase, the possibility that a cell could see a low frequency re-integration of a removed section into the host genome, and subsequent re-activation should be eliminated for all practical purposes.
This system would be placed in tandem on a plasmid so that both would always be present in every transfected cell.
Together with a sequence to compensate for viral load knockdown of GHRH, and a set of coding sequences for synthetic intracellular antibodies, this should achieve long-term knockdown of HIV. This should be capable of reversing late stage HIV/AIDS.