He should have listed the airspace by name..
did he? A Restricted area or MOA?

Nope. Just "airspace closure".

He cannot clear non participating IFR aircraft through an
active MOA. Non Participating means that you are not
part of those that are reserving the MOA.

My understanding is that IFR traffic can be cleared through a MOA if
ATC can ensure separation, so presumably there are some cases when
they can, and some cases when they can't. I wonder what defines which
case it is?

I'm surprised he offered traffic advisories while you were in the MOA.

Yep.

Perhaps he knew that those reserving it were not
there yet, but it had "gone hot" and he could not
sued it for IFR traffic.

Would make sense.