chrisva, regarding a fullscreen recommendation where the player is playing at a sizer smaller than the page itself and then the user clicks (potentially while the media is playing) to go fullscreen: you have 2 overall options:
1) Recreate the player and seek to the correct position (use StartupPosition for this) to resume just like you are doing. You could also navigate to a new page if you wanted to record the action in navigation history. On a side note: navigating to a new
page would also probably resolve the tooltip artifact issue that you are seeing.
2) Position/host the player on your page in a way that would allow it to grow to consume the full screen. This route may require you to make compromises to your page layout but will offer the user the best experience because the media never has to stop and
restart. Here's another thread on one way to accomplish this.
http://playerframework.codeplex.com/discussions/360948. Note: this route may not be possible depending on what else you require on your page.
Unfortunately, there is no way to easily take a UIElement in Xaml and force it to automatically go full-screen.