Update: I ended up replacing the valve this weekend. After examining it more closely, there was significant fluid on the back of the valve, near the manifold. The hose connections themselves seemed to be dry. So my best guess was that the leak was coming from where the manifold attaches to the valve assembly.
Replacing it was a bit messy but straightforward. I clamped off each of the hoses, although none sealed perfectly. Working fast I lost a few quarts of coolant.
I drove around extensively on Saturday to help bleed the system and, after the level initially dropped, it has been holding steady.