0 baht needs to season for 2 months in thai bank account. I am in a similar situation myself. A letter from embassy should be good for another 30 days and thereafter until crisis has passed. I hope!
The baby will be British and require a Brit passport in the first instance to travel, thereafter dual nationality would doubtless be the best case scenario for the child. Can you claim child benefits and other assistance from brit gov? I think i Thailand it is around 600 bht/month for 6 months. Good luck!
They are not fond of issuing emergency travel docs, especially if u r not going home soon. They may tell u to apply for a new passport which will take about 2 weeks.