Perhaps I have been barking up the wrong tree with the martyrdom argument.
You have indeed.
It may be that the risks you mention are eliminated by internal evidence. For example, in 1 Peter the author talks about it being near the time when he will die. This is consistent with what we know about Peter's fate, and so this detail adds to the evidence for the letter not having been made up.
This approach is hopelessly self-referential, since if there is a risk of mistakes or lies in these accounts then the details contained in them are the most likely elements to be wrong.
So, for instance, how do you know that the point you highlight here (that Peter refers to his imminent death and then soon afterwards is executed) wasn't added retrospectively well after his fate was known? If so, then your point about Peter being aware of his impending demise being somehow significant is weakened given there is a risk of fabrication that, from this distance, you probably can't exclude.
As such, and while the stories in the NT might chime with you on a personal basis, the details (such as what Jesus is alleged to have actually said) can't be demonstrated to be factually true to the extent of being historical fact (even allowing for translation issues): after all, if someone decades later decided to put certain words into the mouth of Jesus for effect while writing up the NT accounts ('Blessed are the' etc) how would you ever know?
At the very least this is a risk, since it is known that humans can make mistakes, exaggerate and tell lies, and since this is a risk that you can't demonstrably exclude then it weakens the case for the contents of the NT being historical fact/literally true even if you do find these stories to be personally inspiring.