There's a difference between "wants" and "needs." Sex is important, and easily jumps from a simple want to a grinding need. In my marriage, I've always been the one who needs more.
I would never leave my life partner because he's not as available as I need, but there have been long stretches – years – when my needs simply fell off the map. He was raised in a sexually-suppressed home, and figured it shouldn't be necessary. I suffered intensely, and that was not optimal for our relationship. My beloved could not relate to my need, and as long as he kept up his end of our mutual responsibilities, he figured I should be fine. I struggled for years to "let it be fine," but my stress kept bubbling up through other small cracks. (Added: And yes, self help has always been available to me, but didn't begin to address the missing intimacy.)
Fortunately, they were small cracks, and our mostly-wonderful marriage of 32 years has survived. And somehow, some way, this adorable man found his way to a new physicality that has pumped some real juice into our lives. He's amazed to find that it's been good for me, for us, and for him!
Because your husband keeps expressing this need, tells you what it would mean to him, AND pitches in to help relieve your household stresses, I'm finding it hard to understand your "I'm fine, so why isn't he?" position. It's just so extremely one-sided. Yes, you're over-extended and tired, and yet you have also reported that he's put out a great deal of effort since last summer to make more intimacy possible. He's possibly over-extended and tired, too, and yet he's needing more physical connection with you.
I've got to wonder whether you're genuinely enjoying the sex you do have. If not, putting it on the calendar isn't going to make your half of it any better. What would you need to help you get more joy from the experience? A break in daily routine? A glass of wine? A relaxing back or foot rub? More or different foreplay? If you're simply not feeling sexy, can you give him suggestions about how to help you get there?
By laughing his expressed needs off as "wanting" what he can't have, you are dismissing something that might be a source of genuine suffering for your partner, who has pledged to have sex only with you.