Fix serialization of question state.

Summary:
This fixes some issues with D13740 by moving the logic around a little
bit. Previously the widget props were set inside of `getInitialState`
which prevented the logic from firing when other functions used
`_getInitialWidgetState` to clear the shown widgets. Now the
logic is nestled in `_getAllWidgetStartProps` which should ensure it's
always fired at the right time.

Test Plan:
Navigate around in new full-screen SAT UI and observe that state is
saved and loaded correctly.

Reviewers: dylan, aria

Reviewed By: aria

Subscribers: #sat

Differential Revision: http://phabricator.khanacademy.org/D14069