MySQL:suma fechas y horas sin contar los períodos superpuestos dos veces

Bien, insisto seriamente en que pruebes esto de todas las maneras antes de usarlo en producción. Prueba especialmente qué sucede si hay MÚLTIPLES superposiciones durante 1 período de tiempo.

Lo que hace esta consulta es calcular la duración de cada período de tiempo y cuánta superposición existe con otros períodos de tiempo que tienen una identificación más alta.

select
    t1.id,
    t1.start_time,
    t1.end_time,
    t1.end_time - t1.start_time as duration,
    sum(
          if(t2.start_time <  t1.start_time and t2.end_time >  t1.end_time  , t1.end_time - t1.start_time, 0) -- t2 completely around t1
        + if(t2.start_time >= t1.start_time and t2.end_time <= t1.end_time  , t2.end_time - t2.start_time, 0) -- t2 completely within t1
        + if(t2.start_time <  t1.start_time and t2.end_time >  t1.start_time and t2.end_time   < t1.end_time  , t2.end_time - t1.start_time, 0) -- t2 starts before t1 starts and overlaps partially
        + if(t2.start_time <  t1.end_time   and t2.end_time >  t1.end_time   and t2.start_time > t1.start_time, t1.end_time - t2.start_time, 0) -- t2 starts before t1 ends and overlaps partially
    ) as overlap
from
    times t1
    left join times t2 on
        t2.id > t1.id --  t2.id is greater than t1.id
        and (
               (t2.start_time <  t1.start_time and t2.end_time >  t1.end_time  ) -- t2 completely around t1
            or (t2.start_time >= t1.start_time and t2.end_time <= t1.end_time  ) -- t2 completely within t1
            or (t2.start_time <  t1.start_time and t2.end_time >  t1.start_time) -- t2 starts before t1 starts and overlaps
            or (t2.start_time <  t1.end_time   and t2.end_time >  t1.end_time  ) -- t2 starts before t1 ends and overlaps
        )
group by
    t1.id

Entonces, lo que quieres tener al final es esto:

select
    sum(t.duration) - sum(t.overlap) as filtered_duration
from
    (
        OTHER QUERY HERE
    ) as t

Así que al final tienes esta consulta:

select
    sum(t.duration) - sum(t.overlap) as filtered_duration
from
    (
        select
            t1.id,
            t1.start_time,
            t1.end_time,
            t1.end_time - t1.start_time as duration,
            sum(
                  if(t2.start_time <  t1.start_time and t2.end_time >  t1.end_time  , t1.end_time - t1.start_time, 0) -- t2 completely around t1
                + if(t2.start_time >= t1.start_time and t2.end_time <= t1.end_time  , t2.end_time - t2.start_time, 0) -- t2 completely within t1
                + if(t2.start_time <  t1.start_time and t2.end_time >  t1.start_time and t2.end_time   < t1.end_time  , t2.end_time - t1.start_time, 0) -- t2 starts before t1 starts and overlaps partially
                + if(t2.start_time <  t1.end_time   and t2.end_time >  t1.end_time   and t2.start_time > t1.start_time, t1.end_time - t2.start_time, 0) -- t2 starts before t1 ends and overlaps partially
            ) as overlap
        from
            times t1
            left join times t2 on
                t2.id > t1.id --  t2.id is greater than t1.id
                and (
                       (t2.start_time <  t1.start_time and t2.end_time >  t1.end_time  ) -- t2 completely around t1
                    or (t2.start_time >= t1.start_time and t2.end_time <= t1.end_time  ) -- t2 completely within t1
                    or (t2.start_time <  t1.start_time and t2.end_time >  t1.start_time) -- t2 starts before t1 starts and overlaps
                    or (t2.start_time <  t1.end_time   and t2.end_time >  t1.end_time  ) -- t2 starts before t1 ends and overlaps
                )
        group by
            t1.id
    ) as t