It depends what you consider the outcome to be, by virtue of being a 39 y/o with early recurrent and possibly oligometastatic disease he is in the definitively palliative-intent treatment category so everything is a long shot.
Really the best and only chance for curative intent with most cancers is radical resection with negative margins which unfortunately did not work here (most likely due to micrometastatic disease and perineurial invasion). All of these new and fancy systemic options are not believed or intended to be curative-intent.
If we're talking about meaningful prolongation of life the best treatment would be a PD-L1 inhibitor like pembrolizumab if he has expression. He doesn't mention systemic/immunotherapy in his post but on the donation page his brother does so I'm unsure if he's in the early resistance/treatment failure arm for pembro, if that's the case it's very devastating.
He's correct that gem/plat chemo isn't great but it's something. Patients in his position are best served in clinical trials (also in the treatment guidelines).
With that said it also seems he had an aggressive bone cancer in his childhood, this suggests something unique to this person (e.g. some genetic driver mutation or hereditary cancer syndrome) that may complicate any of this prognostication. Unfortunately something very atypical and aggressive is happening in this person.
H&N SCC in younger patients or HPV+ usually has good outcomes.
Given his history it's probably not relevant to this case but best advice for any HN reader is to go get your HPV vaccine and reduce the risk of SCC.