After much investigation, I think this is the best option for now.
We might need to patch sqlalchemy or switch to refcounting.

The issue is that there's a dangling cursor that's left open, and
under cpython it will get closed quickly.  But for us, it's left open,
which keeps the connection open.  This leaves the table its referencing
locked.  But only in old versions of sqlite!  Newer versions are smart
enough to know that 'select current_timestamp() from table' does not
need to lock the table, so even though that select statement is still
running, it doesn't end up locking the table.

PyPy has a different issue with the test, where it closes the cursor too
early (not sure why).