As the Mother of two girls, who were 3 and 7 when their Dad and I divorced, I never coddled them. Not that you are - but you are offering a lot of reassurance and this need is only escalating...have you stopped to think it may be manipulation and it is working?
Just a different viewpoint here, WTBH, but you seem to think they are so damaged and maybe you are treating them as such?
I would humbly suggest instead of the reassurance - state once, in a very firm not-kidding-around voice that you have heard enough, you have explained over and over again, and you'll hear no more of it.
I did this recently to my 18 yr old, who is anxiety prone - to stop asking me if she is overweight - that if I think she is overweight, I will let her know. In the meantime, not another word. Period. She has not said anything since. Sometimes we have to be firm with our kids and behaviors that are not healthy.