Great analogy. You gave an inspiring write-up of it. There are clear parallels to mental health and depression in the episode and I see the chronic illness ones now too.
This is the best episode of any era, by the way. And I don't just mean of Doctor Who. I rewatch it often. And Peter is an underrated Doctor by the way. I love Moffat's writing, but I think he miscalculated with the beginning of this Doctor. He was purposefully made unlikable initially to contrast with Matt Smith and give him an arc. But it turned away a number of viewers. It's a shame because he turned into my favorite Doctor of all time.
There. I said it