PostgreSQL – Select Using Lateral

This was rather longshot but since the OP says it worked, I'm adding it as an answer (feel free to correct it if you find anything wrong).

Try to break the internal query into three parts (INNER JOIN, LEFT JOIN with WHERE IS NULL check, RIGHT JOIN with IS NULL check) and then UNION ALL the three parts. This has the following advantages:

• The optimizer has less transformation options available for FULL joins than for (the more common) INNER and LEFT joins.

• The Z derived table can be removed (you can do that anyway) from the view definition.

• The NOT(pe.ThisThing = 1 AND se.OtherThing = 0) will be needed only on the INNER join part.

• Minor improvement, the use COALESCE() will be minimal if any at all (I assumed that se.SEId and pe.PEId are not nullable. If more columns are not nullable, you'll be able to remove more COALESCE() calls.)
  More important, the optimizer may push down any conditions in your queries that involve these columns (now that COALESCE() is not blocking the push.)

• All the above will give the optimizer more options to transform/rewrite any query that uses the view so it may find an execution plan that indexes on the underlying tables can be used.

In all, the view can be written as:

SELECT 
    se.SEId + '-' + pe.PEId AS Id,
    se.SEId, pe.PEId,
    pe.StaffName, 
    pe.EventTime,
    COALESCE(pe.EventType, se.EventType) AS EventType,
    pe.Duration,
    COALESCE(pe.Data, se.Data) AS Data,
    COALESCE(pe.Field, se.Field) AS Field,
    pe.ThisThing, se.OtherThing,
    DATEADD(minute, pe.Duration, pe.EventTime) AS EventEndTime
FROM PE pe INNER JOIN SE se 
  ON pe.StaffName = se.StaffName
 AND pe.Duration = se.Duration
 AND pe.EventTime = se.EventTime
WHERE NOT (pe.ThisThing = 1 AND se.OtherThing = 0) 

UNION ALL

SELECT 
    '0-0',
    NULL, pe.PEId,
    pe.StaffName, 
    pe.EventTime,
    pe.EventType,
    pe.Duration,
    pe.Data,
    pe.Field,
    pe.ThisThing, NULL,
    DATEADD(minute, pe.Duration, pe.EventTime) AS EventEndTime
FROM PE pe LEFT JOIN SE se 
  ON pe.StaffName = se.StaffName
 AND pe.Duration = se.Duration
 AND pe.EventTime = se.EventTime
WHERE NOT (pe.ThisThing = 1)
  AND se.StaffName IS NULL

UNION ALL

SELECT 
    '0-0',
    se.SEId, NULL,
    se.StaffName, 
    se.EventTime,
    se.EventType,
    se.Duration,
    se.Data,
    se.Field,
    NULL, se.OtherThing, 
    DATEADD(minute, se.Duration, se.EventTime) AS EventEndTime
FROM PE pe RIGHT JOIN SE se 
  ON pe.StaffName = se.StaffName
 AND pe.Duration = se.Duration
 AND pe.EventTime = se.EventTime
WHERE NOT (se.OtherThing = 0)
  AND pe.StaffName IS NULL ;

Here's how i got it to work:

create table tableone (id int, value int)
insert into tableone values (123,     1);
insert into tableone values (123,     8);
insert into tableone values (234,     8);
insert into tableone values (456,     1);
insert into tableone values (876,     5);
insert into tableone values (876,     1);
insert into tableone values (765,     8);
insert into tableone values (765,     5);
Select a.*
from tableone a
left join tableone X on a.id = x.id and x.value = 8
Where a.value = 1
and X.id is null
drop table tableone