Pipe stdout and stderr through ssh - bash

Question

Consider the following example:
{ echo 1 | tee /dev/stderr 2> >(sed -e 's|1|err|' >&2) 1> >(sed -e 's|1|out|') ; }
which prints
out
err
Note that out out is printed on stdout and err on stderr.
Question: How to do this remotely via ssh?
More precisely, how to run
ssh host 'echo 1 | tee /dev/stderr SOME_MAGIC_HERE'
st. again out/err pops up on stdout/stderr (for an appropriate bash magic SOME_MAGIC_HERE).
Clearly, the following works:
ssh host 'echo 1 | tee /dev/stderr' 2> >(sed -e 's|1|err|' >&2) 1> >(sed -e 's|1|out|')
But that executes sed locally, and I'd rather want to do that remotely on host.

Answer 1

after the update:
ssh host 'echo 1 | tee >(cat - | sed -e "s|1|err|" >&2) | sed -e "s|1|out|"'
out
err
The idea is to use <pipes> | for processing /dev/stdout and use process substitution in combination with tee to create the /dev/stderr part.
Now it works as expected:
$ ssh host 'echo 1 | tee >(cat - | sed -e "s|1|err|" >&2) | sed -e "s|1|out|"' > /dev/null
err
$ ssh host 'echo 1 | tee >(cat - | sed -e "s|1|err|" >&2) | sed -e "s|1|out|"' 2> /dev/null
out
original answer:
The following command executes by changing your <single quotes> into <double quotes> :
ssh host 'echo 1 | tee /dev/stderr 2> >(sed -e "s|1|err|") 1> >(sed -e "s|1|out|")'
but this has everything in /dev/stdout. Example:
$ ssh host 'echo 1 | tee /dev/stderr 2> >(sed -e "s|1|err|") 1> >(sed -e "s|1|out|")' > /dev/null
$ ssh host 'echo 1 | tee /dev/stderr 2> >(sed -e "s|1|err|") 1> >(sed -e "s|1|out|")' 2> /dev/null
out
err
and this is exactly what your original command does on the host system:
{ echo 1 | tee /dev/stderr 2> >(sed -e "s|1|err|") 1> >(sed -e "s|1|out|") ; } >/dev/null
{ echo 1 | tee /dev/stderr 2> >(sed -e "s|1|err|") 1> >(sed -e "s|1|out|") ; } 2>/dev/null
out
err
The ssh program normally handles the passing of /dev/stdout,/dev/stderr and /dev/stdin correctly:
$ ssh host "echo 1; echo 2 > /dev/stderr" > /dev/null
2
$ ssh host "echo 1; echo 2 > /dev/stderr" 2> /dev/null
1