Try using the "Restart MediaPortal on resume..." setting in the MP config and disable the MST's restart for MP.
At the risk of sounding like a total noob, is this something that's been introduced in an SVN since 0.2.3.0 Final (which is what I'm running)? Or is it something to do with TVE3 (I'm running TVE2)?
Yes, it's only available in the SVN versions.