TSQL selecciona una o varias filas para unir

Puede filtrar direcciones fácilmente ([group] IN (48,59,60,87) OR Verified = 1) , pero ajustar TOP 1 haría que las cosas fueran ridículas (TOP (case when [group] IN (48,59,60,87) then 1 else (select count(*) from addresses where order_Id = o.order_Id) end) . Así que te propongo que hagas union all pero solo para direcciones:

SELECT TOP 1000 o.order_Id
              , a.Address_Id
              , a.Zip
            --, *
FROM orders o
CROSS APPLY
(
 select TOP 1
        a.Address_Id,
        a.Zip
   from address a
  WHERE a.order_Id = o.order_Id
    AND o.[group] IN (48,59,60,87)
  ORDER BY case a.Type 
                when 'D2' then 1 
                when 'K1' then 2 
                else 3 
            end,
        a.ADD_DATE
  UNION ALL
 select 
        a.Address_Id,
        a.Zip
   from address a
  WHERE a.order_Id = o.order_Id
    AND o.[group] NOT IN (48,59,60,87)
    AND Verified = 1
) a
WHERE
 o.Status NOT IN (4, 6)
 AND code1='002'
 AND ((code2 IS NULL AND code3 IS NULL) 
    OR (code2 IN ('BIGA', 'BIGP') AND code3 IS NULL) 
    OR (code2 IS NULL AND code3 = 'L'))

PD Si es posible que el pedido no tenga una dirección, reemplace APLICACIÓN CRUZADA por APLICACIÓN EXTERNA.