Apple pie high, I think part of the problem here is that you don't think he would leave, or that it would be morally ok for him to leave. That leaves you with all the power here, because if it would be wrong for him to leave, then he just has to put up with it really doesn't he? And to not do so would make him 'dishonourable'.
You say it would be dishonourable for him to leave, yet by leaving this situation fester for years, your inaction is putting your marriage at serious threat. Knowing that he doesn't want a sex less marriage, but expecting him to endure it for years, is surely a little disnonourable in its own right.
I'm glad you want to take action to try to save your marriage now, but given you've had years to sort it out, and don't seem to have even made basic efforts to figure it out, I certainly wouldn't judge him for leaving.
And yes, it's common for people to go off sex for periods, but not necessarily totally off sex, or for that length of time. Kids, or no kids. It's not about the sex, as such, it's about the intimacy. I could go without sex if I HAD to, and there was a reason for it, but not naked snuggles, kisses, hugs, massage, all the things that make someone not a housemate, but someone you love.
I hope you manage to resolve things, and either manage a happy sexual relationship again, or potentially set your husband free, either from your relationship or monagamy. Either way, it simply cannot continue as it is, it's hugely unfair to him. The pressure of seeming like a 'dick' if he leaves because of your disabled child and mh problems shouldn't be used against the poor guy.
I don't think you're a bad person in all of this, but I do think time has crept on, and things are very unfair as they are.
But I think the first step is to accept that it truly would be perfectly reasonable of him to want to leave.