How to pipe all output streams to another process?

Take the following Bash script 3-output-writer.sh:

lang-bash
echo A >&1
echo B >&2
echo C >&3

Of course when ran as . 3-output-writer.sh it gets the error 3: Bad file descriptor, because Bash doesn't know what to do with the 3rd output stream. One can easily . 3-output-writer.sh 3>file.txt, though, and Bash is made happy. But here's the question: how do I pipe all these into another process, so that it would have all three to work with? Is there any way other than creating three named pipes, as in,

lang-bash
mkfifo pipe1 pipe2 pipe3  # prepare pipes
. 3-output-writer.sh 1>pipe1 2>pipe2 3>pipe3 &  # background the writer, awaiting readers
3-input-reader pipe1 pipe2 pipe3  # some sort of reader, careful not to block
rm pipe1 pipe2 pipe3

?