Você pode tentar usar chrt para alterar a política de agendamento do programa tar para SCHED_BATCH.
De acordo com a página man sched_setscheduler (2)
SCHED_BATCH: Scheduling batch processes
(Since Linux 2.6.16.) SCHED_BATCH can only be used at static priority
0. This policy is similar to SCHED_OTHER in that it schedules the
process according to its dynamic priority (based on the nice value).
The difference is that this policy will cause the scheduler to always
assume that the process is CPU-intensive. Consequently, the scheduler
will apply a small scheduling penalty with respect to wakeup behaviour,
so that this process is mildly disfavored in scheduling decisions.
This policy is useful for workloads that are noninteractive, but do not
want to lower their nice value, and for workloads that want a determin‐
istic scheduling policy without interactivity causing extra preemptions
(between the workload's tasks).
Se você ainda estiver sem sorte, tente o SCHED_IDLE. Isso faria com que este programa só fosse ativado se não houvesse mais nada para executar.
Isso altera a linha de alcatrão para esse lote:
nice -n 15 chrt -b tar -czvf $BKP $PATH_BKP/*.* \