I wouldn't worry about IRIS. While you are right to think about the possibility, it is not common, and should not be an impediment to treat the HIV. I would not prophylax against CMV as you are doing. That practice recommendation changed a few years ago no longer advising it. And glad you are providing Covid vaccine. A third shot of mRNA vaccine will likely be recommended when CDC updates their guidance.
For patients with IRIS, NSAIDs should suffice, but if after 4-6 weeks of increased symptomatic IRIS one could prescribe corticosteroids. I was under the impression that were no longer supporting MAC prophylaxis. Symptomatic MAC Avium treated with Zithromax or Clarithromycin would be a different story.