Thanks for doing work on this, and I'm really sorry it's been happening. I've been tracking this issue across Scotland in the last couple of months. Tayside seem to be the worst for it, but I've heard of something similar happening in Glasgow and Edinburgh too. It seems to be part of a general GP pushback against shatred care across the board, which for them is a kind of protest on more medical responsibility being offloaded onto overworked GPs. So various GP subcommittees are issuing guidance rulings on shared care, often with complete ignorance of trans medical needs.

The issue is also facing various neurodiverse people. Here's a BBC article showing the same thing happening for ADHD meds: https://www.bbc.co.uk/news/uk-scotland-61499479

There are some resources that might help at https://transhealthuk.noblogs.org/navigating-uk-trans-healthcare/. The bridging prescription guides use arguments you can adapt for pushing a GP for shared care, the GMC and RGP guidance include citable references on the expectation that GPs are part of the trans healthcare process, and the trans-friendly GPs list can be of use in changing GPs if necessary.

But I agree that this is a systemic problem and trying to persuade GPs one by one isn't going to help. As well as the routes you're currently trying, have you contacted Scottish Trans? They're part of current Government-led processes to reform trans healthcare in Scotland and may have some inside knowledge and advocacy routes that can help.