I am very sorry to hear about your wife’s condition too and understand how life is with living with the same, first hand. I hope that her condition will improve soon.
Folks on this forum are trying to help you as much as they can with issues you post, and there are a lot of experience here riding and fixing FJRs. Probably more than most mechanics encounter in a lifetime.
I admit, I can get a little enthusiastic and become impatient to hear back from the OP after I post a suggestion that I think would help him. I am sure that I am not the only one to be like that, so bear with us.
In your case the dealer’s explanation didn’t add up - for me at least, and this is why: Your young ‘22 FJR that has just completed a 7K trip and has always ran fine until now, suddenly won’t start after a work shift because of low compression on all 4 cylinders - all at once - due to carbon build-up? It still doesn’t sound right. There is carbon buildup showing on the pictures, for sure, but I still find it unbelievable that it caused a sudden, catastrophic, no-start failure. I would have expected gradual degradation in performance, idling and running issues, etc., first as a symptom of carbon build up that happens slowly over time.