From what I've read,

but it feels sort of like my brain decides it's not wanted and it shuts down to save energy

is the state that meditation is supposed to induce. In other words, a controlled shutdown of certain parts of the brain. Julie Taylor's description of how it feels to have a stroke is pretty much exactly the same as Sam Harris's description of how it feels to meditate.

From a transcript of Julie Taylor's TED talk:

And in that moment, my brain chatter, my left hemisphere brain chatter went totally silent. Just like someone took a remote control and pushed the mute button and -- total silence.

And at first I was shocked to find myself inside of a silent mind. But then I was immediately captivated by the magnificence of energy around me. And because I could no longer identify the boundaries of my body, I felt enormous and expansive. I felt at one with all the energy that was, and it was beautiful there.

Then all of a sudden my left hemisphere comes back online and it says to me, "Hey! we got a problem, we got a problem, we gotta get some help." So it's like, OK, OK, I got a problem, but then I immediately drifted right back out into the consciousness, and I affectionately referred to this space as La La Land. But it was beautiful there. Imagine what it would be like to be totally disconnected from your brain chatter that connects you to the external world. So here I am in this space and any stress related to my, to my job, it was gone. And I felt lighter in my body. And imagine all of the relationships in the external world and the many stressors related to any of those, they were gone. I felt a sense of peacefulness. And imagine what it would feel like to lose 37 years of emotional baggage! I felt euphoria. Euphoria was beautiful -- and then my left hemisphere comes online and it says "Hey! you've got to pay attention, we've got to get help," and I'm thinking, "I got to get help, I gotta focus."

because I'm autistic

Have you mentioned that before? Because I didn't know that about you until now. I'm just guessing, but not being neurotypical may have something to do with your reaction to meditation.