Clearly they are not gender dysphoric so can’t get a GRC by current system (unless they lie and manage to pull wool over eyes of specialists)
Change to self id, that obstacle is removed and opens the doors for anyone with this paraphilia to legally be declared female.
This actually already exists: TRAs have been successful in modifying the criteria for gender identity disorder, such that little is now required for a diagnosis. It's also worth remembering that under Blanchard's typology (and he wrote many of the former guidelines for transition), autogynophiliac and transsexual were not mutually exclusive - indeed, the AGPs were one type of transsexual. AGP itself can cause severe sex dysmorphia (as Datun has mentioned, some even have surgery), although it seems to be on a wide spectrum: from those who fully commit to medical transition, to those who want to occasionally cross dress and be seen by others as a 'pretty lady', to those whose AGP seems to encompass some seriously disturbing behaviour, like the compulsion to involve others in their fetish and enact sexual situations in public.
Regardless, AFAIK under current UK law, trans people don't actually have to have any medical interventions to get a GRC - they just need a doctor's testimony and the approval of a panel (as well as to have 'lived as their chosen gender' for two years, whatever that means). There is already no rigorous gatekeeping in place: it's under the current system that a double rapist was approved for a legal sex change and transferred to a women's prison; and teenage girls are walking out of gender specialists' surgeries with a prescription for testosterone after one visit.
The reasons why TRAs want to do away with even the minimal medical gatekeeping that now exists are twofold, I think. One is a straightforward will to power: they want to control the narrative of transgenderism completely, and they especially want to make the concept of biological sex meaningless in law. This is very important, because as long as sex is recognised legally and socially, it will always be in conflict with 'gender identity', calling into question its validity. The two concepts are inherently oppositional and cannot coexist legally or ontologically, since 'gender identity' itself is the belief that one's feelings override the material reality of sex.
The other reason is that along with the more disturbed non-dysphoric AGPs, many other nefariously motivated males seem to have joined the trans umbrella. I'm increasingly convinced that many of these men aren't even autogynophiles - they just seem to be men who get their rocks off by dominating and manipulating women, pushing women's boundaries, making women uncomfortable, and of course actually assaulting us. Even more disturbingly, a good number of them seem to have pedophilic tendencies. It makes sense when you think about it - 'gender identity' is the perfect cover for predatory men: they get to pose as both harmless and victimised in addition to getting unprecedented access to women and children, since, unlike with regular men, women and children are not permitted to have any boundaries against them.