On brew day simply select a jar, pour off most of the beer, and into the fermenter the slurry goes. 90% of the time there is airlock activity within 6 hours and that is fermenting between 45-47f. Never having to wait for yeast and brewing on a whim are great benefits. I do not miss the starter shuffle!
I do this as well (thanks Bryan). Sometimes I will even pull some wort from the mash tun after the kettle is full and make a vitality starter. Super easy, and the yeast are awake and working by the time they get into the fermenter with the main wort batch.
Just to be clear, you boil the wort from the mash tun before you feed it to your yeast right? I would think it would be full of all sorts of nasties... I tried that one time and realized it was a PITA to boil this runoff and then chill it while watching my brew kettle. So now I simply run off a bit from my BK into a mason jar and chill it after my boil has been going for about ten minutes , its then cooled and pitched into the vitality starter and pitched into fermenter a few hours later.
I only do this when I feel the yeast needs to be roused. For normal gravity ales I simply dump the jar I lazily collected form a prior batch.