Eu não sei por que você está rodando rsyncs de maneira que você está rodando, mas se eu fosse você eu consideraria seriamente outras formas de resolver o problema que não envolvem ter múltiplos rsyncs escrevendo para a mesma árvore de arquivos ao mesmo tempo.
Isto é da página man do rsync na seção --temp-dir:
If you are using this option for reasons other than a shortage of disk space, you may wish to combine it with the --delay- updates option, which will ensure that all copied files get put into subdirectories in the destination hierarchy, awaiting the end of the transfer. If you donât have enough room to duplicate all the arriving files on the destination partition, another way to tell rsync that you arenât overly concerned about disk space is to use the --partial-dir option with a relative path; because this tells rsync that it is OK to stash off a copy of a single file in a subdir in the destination hierarchy, rsync will use the partial-dir as a staging area to bring over the copied file, and then rename it into place from there. (Specifying a --par- tial-dir with an absolute path does not have this side-effect.)