But if I understand you correctly, then you are saying there is no way to get there?

No, I am saying you have to learn more about mozrepl/firefox/javascript and create your own one of these

sub eval_in_page {
    my ($self,$str,$env,$doc,$window) = @_;
    $env ||= {};
    my $js_env = {};
    $doc ||= $self->document;
    
    # do a manual transfer of keys, to circumvent our stupid
    # transformation routine:
    if (keys %$env) {
        $js_env = $self->repl->declare(<<'JS')->();
            function () { return new Object }
JS
        for my $k (keys %$env) {
            $js_env->{$k} = $env->{$k};
        };
    };
    
    my $eval_in_sandbox = $self->repl->declare(<<'JS', 'list');
    function (w,d,str,env,caller,line) {
        var unsafeWin = w.wrappedJSObject;
        var safeWin = XPCNativeWrapper(unsafeWin);
        var sandbox = Components.utils.Sandbox(safeWin);
        sandbox.window = safeWin;
        sandbox.document = d;
        // Transfer the environment
        for (var e in env) {
            sandbox[e] = env[e]
            sandbox.window[e] = env[e]
        }
        sandbox.__proto__ = unsafeWin;

        var res = Components.utils.evalInSandbox(str, sandbox, "1.8",c
+aller,line);
        return [res,typeof(res)];
    };
JS
    $window ||= $self->tab->{linkedBrowser}->{contentWindow};
    # Report errors from scope of caller
    # This feels weirdly backwards here, but oh well:
    #local @CARP_NOT = (ref $self->repl); # we trust this
    
    my ($caller,$line) = (caller)[1,2];
    
    $eval_in_sandbox->($window,$doc,$str,$js_env,$caller,$line);
};
[download]

Okay, you clearly know more than I do, but you apparently enjoy giving cryptic answers.

For all others that might have a similar problem that I had: Using an older version of Firefox fixed it.