Watch losing time and step count at night?

Ok - I'd definitely try a normal clock face just from the app loader then to see if it still gives you the issue.

I thought the clock face only displayed info, and wasn't responsible for actually setting it?

No, it doesn't - I had assumed you were looking at what was displayed on the clock screen, which obviously the clock app is responsible for.

What apps do you have installed? The app loader's 'more' tab can give you a list.

There are some apps (like the time adjustment one) that actually do change the system time (although very few others do). Obviously if those were installed I guess they could be causing you issues.