Ok, I've managed to cobble together a buildbot setup to test the hang myself and have come up with a couple possible solutions.

The first is to change the buildbot service on the slaves to allow desktop interaction.  This way, the tests can actually run.  If that's not possible, it's probably simplest to just pass -u-gui to the buildslaves in question, since there is in fact no gui available.  That should at least fix the test_ttk_guionly problem.

As for the test_tcl problem, how about this patch?  It simply wraps the Popen call in a try/except, and converts to a skip in case of an 'Access is denied' error.