I'm not going to pretend I know much about it because I don't. However would common sense not dictate that offering people a choice which includes a unisex option can enable trans people (or anybody else for that matter) who feel uncomfortable with the current male/female toilet options (I'd imagine because of how other people react) an option to avoid all that and go and use the loo without those issues. I'm not pretending this is a long-term solution but it surely is a better option than having people feeling so uncomfortable with how things are now they are avoiding using public toilets at all?
Personally I feel uncomfortable in unisex toilets so I would continue to use the male loos but as long as we all get the option then surely that's ok?
Most trans people don't have issues with sharing or unisex toilets though, the people against it are from the same vantage point as Rowling, it's these people you need to convince. You're right though, it would make a lot of trans people who are early in their transitions feel better.