A couple more possibilities:

{
    local *STDOUT;
    open STDOUT, '>>', "$logbin/$logname" or die $!;
    # ...
}
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or else

open LOG, '>>', "$logbin/$logname" or die $!;
# ,,,
{
    my $oldout = select LOG;
    # ... log stuff
    select $oldout;
}
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The choice depends most on what fits your program design.

The case you need to worry about with your code is when STDOUT has been redirected someplace else. You want to restore it to what it was when you exit the logging block. Hemce local.

After Compline,
Zaxo