What do you mean when you use the word compromise? If it's allowing some males into female spaces then the compromise is made entirely by women for the benefit of males. If that's not your proposal then why is it incumbent upon women to find the solution. I am defending women's rights, not opposing trans rights.
The government can legislate for all the transrights they want providing it does not come at the expense of women's rights. The Equality Act 2010 gives trans people the same rights as everyone else. In this instance the judge decided the claimant had been discriminated against on the basis of gender reassignment but that is incorrect, the issue arose because of the claimants sex not because of their gender identity. There is already case law on this subject.
Women compromised in 2004 when the GRA was introduced and people incorrectly assumed that a GRC gave a trans person the right to be treated as their acquired gender in all circumstances. It does not, there is provision within legislation to lawfully excluded TW and TM from single sex spaces where there is a "proportionate means to a legitimate aim", changing room would meet that criteria so this problem is entirely of the hospital's own making.
Your final sentence highlights the folly of our current path. When enough piss takers cause enough problems there will be a backlash, if there is violence against TW it will be perpetrated by men, as most violence is, but the people with gender dysphoria can't just walk away from their condition anymore than I can walk away from being female. If people actually cared about this group of people they would recognise the harm the piss takers are doing and stop indulging them.