Engineered CD8 T-cell therapy for HIV infection
People in the comments suggest that this would "Drive the patient into AIDS sooner", or that this will be ineffective because of dormant virus.  Neither is correct.

The question is asking about engineering CD8 with engineered T cell receptors specific for HIV.  This is a logical approach, and multiple groups have tried it:


In Vivo Suppression of HIV by Antigen Specific T Cells Derived from Engineered Hematopoietic Stem Cells
Reconstitution of anti-HIV effector functions of primary human CD8 T lymphocytes by transfer of HIV-specific alphabeta TCR genes
Development of CD8+ T cells expressing two distinct receptors specific for MTB and HIV-1 peptides
T-cell engineering by a chimeric T-cell receptor with antibody-type specificity for the HIV-1 gp120


A brief search on Pubmed will turn up many other articles. Some of these approaches have entered clinical trials; for example:


Redirected High Affinity Gag‐Specific Autologous T Cells for HIV Gene Therapy


The problem with this approach is not that it will "drive the patient into AIDS sooner".  A strong CD8 T cell response controls HIV well, and although it might be one contributor to CD4 T cell loss it's no longer believed that it's a major cause, especially in the early stages of HIV infection.   

The general problem with CD8 control of HIV is that the virus is capable of mutation to avoid control by CD8s. Essentially, every case of HIV is effectively controlled by the CD8 T cell response in the early stage of infection, but the virus then mutates and escapes control, then the CD8 response adapts and controls the virus once again, and the virus mutates and escapes ... This can and has been tracked in many patients, showing repeated rebounds of the virus in the blood correlated with CD8 changes.

Better CD8 control of HIV is linked to a broader CD8 response -- that is, attacking many viral proteins, so that viral escape requires multiple simultaneous mutations (exponentially more difficult for the virus).  (Alternatively, the CD8 response can attack a small number of proteins that are very constrained, so that the virus can't successfully mutate them.  However, for reasons related to MHC restriction, that seems to only work in a small minority of people.)

An engineered CD8 T cell response will inevitably be to one or a small number of viral proteins.  That's conceptually similar to the natural situation following HIV infection, meaning that the outcome could be the same -- viral mutation and immune escape. 

Because engineering the TcR means you can pick your targets rationally, you might be able to do better than the natural situation, but it's not obvious.  Overall, the fact that groups have been working on this approach for decades, without a breakthrough cure yet, suggests that it might be useful but isn't going to be a slam-dunk.