PhD transfer during first year
You can take the best of the two worlds. Get all your PhD training (by the way, what does it mean?) at WashU and then start a clean research cooperation with the relevant people at USC, while being at WashU.
You can do that by applying for exchange funds, by &quot;stalking&quot; people from USC at conferences ... there are many different ways, but for sure you want to keep bureaucracy and practical hurdles at a minimum, so stick with your PhD program at WashU.