If you aren't familiar with drawboring, this won't make much sense, but there are plenty of good videos explaining it out there on the web. A little peg is going to squiggle through offset holes, holding the yellow stick over the purple tenons. Simultaneously, the width of the hole in the tenon will accomodate the purple board as it gets wider and narrower with the seasons. At least that's the theory.
|See how the hole doesn't quite line up? That's the key to drawboring.|
I think it's going to work, but I've never actually seen these two combined. I'm going with a very small offset just to be safe.
Incedentally, those Woodtek drill bits that are meant to cut sideways work superbly in an eggbeater drill. You need to get it spinning fast before applying sideways pressure (it's similar to handsaw technique), but then it is so controllable that I doubt those bits will ever see the inside of a power drill chuck again.