So, I originally removed the domain from Cloudflare but kept the NS pointed to Cloudflare. There was no change in behavior. Doing a dig on the domain name returned the correct Dreamhost IP as returned from Cloudflare namservers. How? I have no idea how. I then readded the domain, and Cloudflare picked up the domain records it already knew, as in nothing had changed. (All other previous settings were still there as well.)
I had a closer look at each DNS entry and saw I had two IPv6 entries for @ and www. So, to be extra neurotic, I removed the IPv4 and IPv6 @ and www entries and then readded them. Doing a dig on the domain to the Cloudflare nameservers now shows the proxy IPs.
If this is correct, the problem is on your Dreamhost site.
You may still want to take a look at the following #tutorial. Liberate the Hostname is often the right tool for to fix an unwanted redirect of a domain that was previously used with a Cloudflare for SaaS partner like Shopify or ClickFunnels.