Hi M
” I wonder if I should simply accept that this is my true weight, and not try to lose more?”
NO. You can get down to a BMI of 25 or 24 if you want. I have been stuck a couple of times too. You just need to examine more carefully what you are eating and drinking and how you are fasting. I have extended my fast to 36 hours and I am sure that will help me and you. I start my fast some time between 10pm and midnight and today it is nearly mid-day (in Spain) and I have only eaten an orange so far after a full day on diet yesterday. We are entertaining friends tonight and are having German-style cheesecake for dessert. I can behave for a reward like that. Next week I might do 3 days fasting. My aim is to get to a position like Michael Mosley, where I just fast one day per week. I exercised more than I have done for a long time last week including on diet days and feel much better for that too. Keep a self-critical attitude to your diet and you will win.
Oh. and keep busy – mentally and physically.

As Mark suggests, you need to look at what you are eating and drinking. My bet is on eating too much on non fast days which is a common issue as most of us are overweight because our idea of normal is actually overeating.
A fast day should start after dinner on for example, Sunday and not end until you eat on Tuesday. There are many on here who don’t break their fast before lunchtime after a fast day, and many who don’t eat before lunchtime on any day.
I’m sure if you count calories for a week and check your TDEE you’ll find you’ve been eating too much and will be able to make the necessary changes.
If you’ve not calculated your TDEE yet go to the top of the page and click on “how it works”
It pays to under estimate your exercise or eat less than your TDEE.

Good luck.