In fact, I found the answer myself:
as soon as one variable is output that has multibyte characters in it, output switches to Unicode an all other (ISO-Latin1) characters are output as Unicode as well.
To prevent this from happening, rather than writing
print OUT $myunicodestring;
print OUT $converter->convert("blöd");
which wouldn't have worked anyway, I now use
$myisolatinstring = $converter->convert($myunicodestring);
print OUT $myislatinstring etc.
using Text::iconv
now all works fine.
Thanks,
Björn