I finally got around to shutting down my DreamHost account. I poked around a bit in the control panel and didn’t find a way to cancel the account. I started to file a support ticket and their ticket tool pointed me in the right direct to cancel the account myself. Turns out I was on the right page already, just missed the tiny link for end my account.
Actually ending the account was a simple as checking a checkbox, entering my password, and answering a few questions in an exit survey. Props to DreamHost for making super easy and not dragging things out and having me wait forever on the phone to talk to humanoid.