How would I know?

In your code, here:

{
    # reduce bogus warnings
    no warnings 'uninitialized';
    

    # get past the header
    ( $token_type, $argument, $parameter ) =
    $tokenizer->get_token() until
        ($token_type eq 'control' and $argument eq 'par');
}
[download]

you call ->get_token(), which reads a set of tokens and throws them away.

Maybe consider changing your code to:

my @tokens;
{
    # reduce bogus warnings
    no warnings 'uninitialized';
    

    do {
    # get past the header
      ( $token_type, $argument, $parameter ) =
      $tokenizer->get_token();
      push @tokens, [$token_type, $argument, $parameter];
    } until ($token_type eq 'control' and $argument eq 'par');
}
[download]

and then, when writing your output document, first output all the saved stuff from @tokens.

I don't know RTF and I don't know your input document and I don't know your wanted output stuff, so I can't give much more concrete help.

While you cannot help me with the first issue, you can help me with the second and third issue by posting a short example of your RTF input and wanted RTF output, especially including a part that contains random coloured stuff or whatever you want to keep. If I have this, I guess that would be enough for me to fake knowing RTF enough to keep the formatting.