You don't sound like a broken record you just sound like you've done everything you can think of to change the dynamics to improve your M and yet that one last piece is still missing.
The problem is that IT IS a very important piece for you and it is not okay for you to continue forever with that piece still missing.
I've got friends of all ages and some are very HD some are very LD some are ND but all of them have been prepared to have some form of SL. Even the ND one is prepared to give a HJ but that to me is pity sex and IMO is not what you are looking for here.
That said the fact that your W isn't even prepared to give anything to you means that your R while you think it is good is pretty one sided IMO.
So far none of her reasons hold much water. She doesn't sound to me like it is a body image problem if she lets you see her in the bath or walks around naked. I have way more body image problems and could never walk around naked mind you I do have 3 adult sons who would freak out LOL. Strangely I always sit and chat to my H when he is in the bath but I always lock the door when I'm in there myself. Hmmmm maybe I have some hang ups I need to work on myself. Point is I still enjoy sex even though I'm not keen on the saggy bits or stretch marks. So body image an excuse ....yes.
The heavy periods hmmmm how exactly do you know whether thats true? I mean she could tell you she is having a heavy period that lasts 2 wks but short of youchecking that could be an excuse. Fair enough giving her the benefit of the doubt and she is seeing a gyny doc there may be fibroids or something that causes it BUT again NOTHING to stop her giving you a HJ/BJ when she is having her period. NOTHING !!!! Except she does not see your needs as being important and that is what SHE has to change.
She doesn't like you bringing the subject up then tough. She is not going to be happy when you tell her you've had enough and walk out the door. She's controlling you by her rejection and thats probably why it felt good you being the one to turn away and not cuddle her even though she was sending out the signals that she wanted you to. Dangerous because once you start withdrawing yourself it really is the end in sight.
I know you don't want to rock the boat right now while you work on improving your finances so that you have the option of leaving. Do you think that if your W knew that you are prepared to walk anything would change or do you think she would just switch off even more? Bit of a catch 22 here.
You seem to sometimes be telling yourself that this is not a good enough reason to leave what is otherwise a good relationship. Don't buy that one because it is a very good reason and eventually resentment will colour all the good things I'm amazed it hasn't already.
You probably wouldn't tell the kids the truth as in you couldn't stay in a SSM any more. It would be more likely you would bend the truth by saying as much as you love their mum you just can't live together any more. You would tell them that you love them and will always be there for them. Depends how amicable it is.
Hope against hope someone else can come up with some ideas how you could change this. Just keep talking to her and trying to get her to be honest with you.