Proper update:
I thought pretty carefully about whether to go in gender-neutral clothing, e.g. jeans, hoodie and trainers, but decided that it would be far more effective if I clearly presented as a woman. So I wore a pencil skirt, tights, high heels, blouse, cardigan, wore my long hair down, applied makeup and carried a handbag.
The two managers had sent me an email asking to push the meeting time back a bit but I was too busy MNing
so didn't look at my emails this morning and missed it. They squeezed me in anyway and we had a good chat. They were both very pleasant and polite and took careful note of my questions (in email above).
The manager leading the meeting was very focused on understanding my individual concerns. I said that I identified as a man and that I was not planning to change my appearance or seek hormone therapy or surgery to alter my appearance. She wanted to understand why I was interested in attending the men-only swimming sessions, which changing room, toilets and showers I would prefer to use and if I wanted to swim topless. I said that I wanted to know whether I could attend the men's sessions because they were specifically provided and that I wanted to use the men's single-sex facilities and swim topless.
They couldn't give me a decision today, which was a bit disappointing, but they did thank me for coming in to meet them and said that I can expect a response in a couple of weeks once their top management have had a chance to have a look at it. As a decision is still to be made, I took the chance to bring up the gap between the Swim England guidance and the EA exemption. I've put it in my email again so it's uber-clear that they have other options than embracing self-ID.
To be honest, it was really difficult for me to act against character and I really had to be strict with myself to ensure that I made my preferences in accessing men's spaces crystal clear. I'm sad that those really nice people I met are now going to think of me as utterly selfish. Do pro-self ID TRAs really think they're so in the right that they don't notice other people's upset and discomfort, or do they just not care?