According to this guide (below), there’s two other non-stimulants you haven’t tried yet. I’ve read that many people with inattentive subtype (ADHD-I) respond to guanfacine plus a stimulant. One of Russell Barkley’s YouTube videos says they affect different parts of the brain in a complementary way particularly effective sometimes for ADHD-I.
I don’t think there’s anything unreasonable about adding an SSRI for your son, but it seems reasonable to also ask whether he could try all the non-stimulant options first before considering adding an SSRI on top of what he’s taking now. In fact, why not exhaust all the ADHD medication options (stimulant and non-stimulant) before adding an SSRI if the child is happy and not anxious when not on medication? For example, Adderall made my daughter irritable, but Vyvanse and Dextroamphematine (in the same medication class) do not. What medications work best is such an individual thing, and you don’t know until you try them all. I can’t imagine the doctor and NP insisting you start him on an SSRI without allowing you to try all the non-stimulant and stimulant ADHD medications first. I’ll bet they would be open to that if you ask them if that would be okay with them.