I bet that the biggest contributor to this is that you are "suffering from buffering". When the output from dispatcher is going to a terminal, then that output is "line buffered" which means each line of output appears immediately. When that output is going through a pipe, then it is "fully buffered" which means no output will flow into the pipe until the internal I/O buffer fills up (for example, no output until at least 4KB of output is produced and then the first 4KB of output goes into the pipe at once).

The easiest improvement is to just add $| = 1; to your dispatcher script.