A quick smoke test of the patch (solely on OS X) looks like it works pretty well.  Not surprisingly, it doesn't fix anything when using the deprecated -n ("no subprocess") option but that's not a problem.  One more serious issue is that, depending on the length of the output produced, the IDLE shell prompt ('>>>') for the next command may appear out of sync, interspersed within the displayed stdout rather than at the end.  And, yes, the os.write(1, ...) to stdout in the same process is an equivalent way to look at the issue and the patch seems to handle that as well.

Nice work, Serhiy!