I'd agree that you should look at ACCA or CIMA qualifications rather than AAT - you can work your way up with experience from AAT but coming from a career change rather than school/University leaver the ability to jump start with higher level qualifications will be better for you.
You can self study the early exams online.
Theoretically, CIMA is more suited for management accounts/analysis roles and ACCA more technical - but in reality you can get exposure to both through the work and take career in either direction.
Month ends can be an issue with holidays - bigger companies are likely to have tight deadlines. Year ends are key too - typically December/Jan or March/April will be busy times.
That said there is lots of flexibility in working from home, for big or small organisations, industry types.
At the very process book-keeping end, there is a threat to job security from automation - but at the personal level and being able to interpret and explain things to clients or colleagues I think it is lower risk.
There are lots of jobs at the moment!
Maths graduates have relatively high exam pass rates - I don't really know why as the hardest maths involved is addition, subtraction and percentages so nothing like degree level!
And you can get payrises and promotions and more interesting work as you progress through the exams- even if you don't complete them all.