@transworld I have mixed feelings here. This seems a little under-researched, but coming from a good place. Collecting personal written accounts could be sensible at a stage where you have a plan in place for what to do with them, but just spamming elected officials with them is unlikely to be effective, and would require getting more explicit consent for that purpose.
The other thing is, an open-ended call for ideas and the single person named here suggests he's not already working with organizations that have work in progress and need boots on the ground. I strongly recommend plugging into existing efforts and organizations. That's not to say don't do what he's proposing -- just don't reinvent the wheel. Work with and learn from people who have been doing this sort of work.
Lastly, I would be remiss if I failed to point out that the US is far from the only dangerous place to be trans, and it will be important to make sure any efforts at making space for refugees from the US don't displace or leave behind people in much more precarious circumstances. I know a non-American trans person who came to the Netherlands as a refugee and found the experience utterly dehumanizing. The details aren't mine to share, but there are plenty of stories out there. I think it makes the most sense to start by addressing known problems with the asylum process, with or without the focus on trans refugees, and to get guidance from current asylum seekers and people recently granted asylum.
I hope this can be taken as constructive criticism. Please send Ned my best wishes for his success in this effort, and my thanks, along with my comments.