@9toenails
Thank you for your interesting post - I enjoy philosophy. I will try to answer some of the points you raise:
"It would not be gaslighting to point out that the bush is in fact a bush rather than a bear. Could that be going on here?"
I am by nature a sceptic, so would say yes, it is possible, just as it's possible I'm not typing this, and that I am a brain in a jar being stimulated by a clever scientist, but I have no particular reason at this moment to doubt any of those things - I merely acknowledge the remote possibility of them.
"Think of another example, anorexia nervosa (a common enough analogy with trans in this regard): a sufferer might describe their experience of themselves as that of a person who is overweight when actually the opposite is the case. What a person with anorexia thinks she is experiencing misrepresents how things actually are."
The analogy with anorexia is spurious. A trans person sees exactly what their body looks like in a mirror - it's that reality that she reacts to. And of course, if you affirm an anorexic, you kill them whilst all the evidence suggests that affirming a trans person saves them so they are clearly not analogous conditions.
"Many other examples; there are those, I am told, who experience themselves as being a reincarnation of some historical figure. And so on."
Again, this is a spurious analogy. Someone with the condition you describe believes themselves to be someone else. This is the opposite of being trans - a trans person knows who they are and they don't conflate themselves with anyone else - they merely observe their gender identity, their body, and the incongruence between the two.
"I am not cannot be mistaken about it seeming to me I see a bear, even though it is actually a bush over there, or about it seeming to me I am Napoleon Bonaparte. And so on."
Those are not comparable scenarios. The impression of a bear is a logical one, derived from what you can actually see - if something looks like a bear, it is reasonable to assume it is a bear until better information becomes available. Seeming to yourself that you are Napoleon, can only be a delusion unless you actually are Napoleon. The former is a healthy mind working logically with the information before it, the latter is an unhealthy mind working from a delusion.
"'I seem to be dead and alive at the same time' could not be true if construed literally; there is no such thing as being alive and dead at the same time."
This is not actually the case - there are several philosophical approaches under which this might actually make sense to some degree. Start with the ship of Theseus and see where it leads you with this. Your body contains almost no matter from the you of 30 years ago. Where is that person now?
"It is possible transgender people make such a mistake, involving contradictions of sex (male/female, man/woman) -- rather than life (alive/dead)."
Trans people don't see themselves as two logically incompatible things simultaneously. Your assumption that they do, may be derived from the assumption that sex is a simple binary. That's not the case. A trans person recognises their physical characteristics - they typically trigger gender dysphoria, and if they weren't aware of them, trans people wouldn't have medical interventions to change them. They also recognise that their gender identity is not congruent with those physical characteristics, although that is a nuanced argument given that gender identity is biological in origin and therefore, to be more accurate, a trans girl is recognising biological characteristics like her penis as well as biological characteristics like her gender identity.