It's a gender recognition certificate, not a sex change certificate. You can't change sex and this is provable fact, whatever TRAs say. So the solution I'd go for is to make clear that sex matters and people are allowed to define themselves by sex, and single sex toilets, changing rooms, prisons, and sports are justifiable.
The GRC should then be clearly defined as a "gender" only change, gender meaning a person's idea of themselves as transgender or wanting to simulate the opposite sex, without that having anything to do with sex itself. Sex remains the same.
Being "transgender" should, and in effect does, mean doing an impression of the opposite sex or being drawn to the stereotypes associated with the opposite sex. (Or if we're including NB, the stereotypes of neither or as it often seems, both.) You shouldn't need a label for deciding not to be a walking stereotype of your own sex - I'm not and I don't. It's very sexist to see things that way at all IMO. But people could choose a GRC so that they can be officially transgender. Not officially the opposite sex.
It's not just that trans ideology is harmful - what's also insane is that it's a huge exception to our standard approach to reality. You can't do this with ethnicity, age, height, disability, your job and qualifications. You can't identify as me and have access to my house. You can't be white and identify as black, or be able-bodied and identify as having CP, however convincing an impression you do. Because that would be madness and anyone can understand why these things would not work out well if they were made into laws.
People can do an impression of someone they're not for whatever reason - for fetish reasons, to gain access to somewhere, or even because they genuinely believe they are something they're not. But everyone knows that doesn't make them that thing. Just because it can happen, and it might be difficult to stop it, doesn't mean it should be made legal.
I can't stop someone declaring they're me, breaking into my house and sitting on my sofa, if they really want to. But it's pretty rare because everyone knows that person would get arrested and people would find the self-identification as someone else outrageous and ridiculous, so there's a stigma attached that stops most people from even going there. It's not about paperwork and inspections to see if they're really me. It's about a total breach of our shared understanding of reality and what people can be, that needs to be mended.