It's finally running! I transferred all the livestock and fixed up the sump last night. Found my pom pom crab in the process--glad he's still alive, but I wish he would come out once in a while.
I wasn't able to fix the check valve--no way to move it down lower to get more pressure--but it does seem to consistently close after a few seconds. I dropped the sump water level by an inch to allow an extra margin.
I don't know much about what my urchin needs. Ultimately it will likely go in the refugium. In the interim, would it be better off in the display tank (live rock, no macroalgae) or the refugium (base rock, macroalgae)?
The old 10G tank, nearly empty:
The new tank in the process of transferring livestock:
The new sump/refugium:
I'll take a picture today of the full system in operation--the lights were already off by the time I took pictures.