I'll try and address this since no one has answered yet.
One of the reasons it would be very hard to justify testing this first as a cure is because AIDS patients are by definition immunodeficient. Their Helper T cells (the CD4s mentioned) are being rapidly co-opted by the virus and subject to destruction. In such an environment it is difficult to mount an immune response because the Helper T cells are so instrumental to enabling the cytotoxic immune responses instigated by this study (the CD8 cells are your cytotoxic "killer" T cells).
Any trial run on humans already suffering from AIDS would be muddied by this effect, where the already compromised immune system cannot mount a robust response even were it able to develop CD8 killer cells specific to the HIV epitope they vaccinate with.
Phase I trials are high risk, and especially for a bootstrapped team like this, have a lot riding on them. An early failure can doom a technology in this industry, so it is important to focus on testing in an environment where you have the best shot at success. Downstream studies can focus on other applications if needed.