Have you tried reopening STDOUT? If you've already got a filehandle, it goes:

open(STDOUT, '>&MY7') or warn "$!";
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otherwise, just open a file for writing normally, using STDOUT as your filehandle. You can save your STDOUT filehandle by

open(SAVE_STDOUT, '>&STDOUT');
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first, then restore it with

open(STDOUT, '>&SAVE_STDOUT');
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after.
Update: Oh, ikegami's looks much easier.