I don't have an intellectual conflict about late term abortions. For me, feminism (and every other movement for equal rights) is about collectively gaining equality of outcome for women, not the defence of any other particular principle. That doesn't involve giving everyone exactly the same rights as each other.
I am not, for example, going to fight for the right for people who are entirely blind to become fighter pilots. In principle this means they do not have equal employment opportunities people who can see, but in reality fighting for such a right would give blind people a right they neither want nor need. It is better to recognise that blind people will not be able to carry out certain jobs, and make sure that the law in terms of reasonable adjustments and benefits for people with disabilities in employment are suitable and adhered to. This creates a sort of compensating situation that allows us to work towards equality of outcome. Not recognising the different wants and needs of disabled people by giving them identical rights rather than contextually beneficial rights would be damaging.
I believe the same for abortion. There may be some circumstances where a woman who previously wanted a baby so continued a pregnancy has a huge change in her social situation, making continuation of the pregnancy highly undesirable for her. But few, if any women, put in that situation would want an abortion for non-medical reasons at 35 weeks. To defend equality of bodily autonomy in that situation is to give most women in that situation a useless right. It would encourage callous behaviour where people can say, well woman X should have an abortion at 35 weeks to avoid that situation so we don't have to do anything about changing the situation.
It is far better for the law to recognise that the vast and overwhelming majority of women would not want to abort at 35 weeks for social reasons, and would be mentally traumatised by doing so. As a consequence, the law limits their bodily autonomy. Women in late pregnancy should then be compensated through contextually beneficial rights by having greater rights to workplace protection, maternity leave, benefits and housing than other people. We are then working towards equality of outcome by not having equality in the principle of bodily autonomy but by giving pregnant women greater rights elsewhere to compensate.
The important point in looking at those factors is that they are all about the wellbeing of women, and balancing the rights given and taken from them, without bringing in the rights of the foetus as some sort of reason for simply disregarding women's rights. The problem with the abortion debate is that it seems to be all about saying women can't have various rights because children are more important, with no regard for women's equality or how to address it at all.
I am not saying that bodily autonomy isn't important and should be disregarded in a cavalier way. But I think there are some rare situations where equality is more likely to be achieved through other means, and there is no reason to defend the principle of bodily autonomy in every single context.
With regard to the woman in question and 16 weeks, I don't know enough about her situation to comment. Presumably the person who does know and has to ethically agree it is in her best interests is her doctor. I suppose it is rather like benefits where we accept that by setting up a benefits system, there will be a few people who will use it in ways we do not like, but it is so important to the wellbeing of the massive number of people who don't misuse it and really need it that we must keep on supporting it and seeing it as a great social good.