It's pointless trying to pin down the language and argue on a level playing field on gender, because gender is a religion.
To have a gender identity of female in a physical body which is male requires the belief that the individual with the gender identity exists separately and independently from the physical body they inhabit.
Otherwise, any feeling a male bodied brain has is, by definition, a male feeling i.e. a feeling a male person is having.
Nothing new about this, many if not most have a similar central belief - that of a non-corporeal "soul". And I've no doubt that many religious people, when thinking about an afterlife, think about continuing to exist in the same basic form, including gender, even if not consciously.
Arguing against 'gendered souls' with facts and figures is likely to be as successful as arguing against any other aspect of a sincerely held religious belief by quoting the lack of physical evidence.
However, we don't need the trans community to stop believing (or stating that they believe) they have changed sex/gender. What we need is for the belief that they have changed gender to be given the weight it deserves - as one belief amongst many, often contradictory beliefs.
We need to challenge why this belief, alone amongst a huge sea of beliefs, is given the status of fact in sections of society. No need to argue with any individual beyond 'I understand you believe that, I believe something else - I'm a gender atheist.'