I do not think that you need a divorce.

What you need, in truth, is some sort of an annulment, since the marriage has never been properly consummated.

That said, you won't prove it after 7 years and with children in tow, so technically speaking, yes, you need a divorce. Think of it as a divorce for practical purposes but as an annulment in your mind.

Regarding "an easy way out" - your problem is that you should not have gotten IN. But you did get IN. So now you need OUT. If you like unsurmountable challenges, then, of course, you do not need to settle for an "easy" way out, but you still need to find some sort of a way out.

I do not understand what actions or proposed actions you consider "selfish". It seems to me that anything that is not 100% extreme martyrdom is "selfish" for you. This is not the standard view of what "selfish" is. So if you
can explain with more detail and depth what would be "selfish", that would definitely help to gain insight into your frame of mind.

In any event, an amicable divorce and an equitable custody arrangement will be fine in terms of how your children will fare.

And you will become available for someone who might actually become attracted to you! And your children will be happier if you see that you are happy.

Regarding "sticking together to work it out" - you can stick together to work out a fair arrangement on how the chores are split. You cannot really "work it out" when the woman has never been sexually attracted to you and continues being uninterested in you. Yet, she says that she loves you. How does she express her love? Usually, people express love in a variety of ways, sexual being one of them.