The trailing edge needed to be removed and both sides needed to be countersunk to accept the dimpled trailing edges on the skins. I ended up purchasing another countersink cage from Cleaveland so I wouldn't have to remove the #30 countersink and reset the cage. For around $30, the additional cage makes sense to avoid having to drill more holes and test the depth in scrap pieces every time I change the countersink.
At first I took the small trailing edge piece from the Van's practice kit and clamped it under the full size trailing edge to square everything off before using the drill. Because the trailing edge is so small I would have to unclamp it, move it down, and reclamp it every couple of countersinks. It was becoming tedious, and I soon realized that this wasn't really necessary. The easiest way to complete this step is to just take the trailing edge in one hand and hold it tight against the countersink cage while drilling it. The countersink bit is held in place laterally by the hole itself, so the countersunk hole will turn out nice as long as the cage is held tight against the surface of the piece.
Turning the piece over and countersinking a few of the holes on the other side of the piece made me realize that the #40 holes get enlarged when both sides are countersunk. I quickly turned to the forums to see if I had made a mistake. From what I could tell the enlargement of the holes not only seemed to be a normal occurrence, but it didn't seem to matter that the holes would be larger than the rivets because the skins on either side are what actually hold the rivets in place rather than the trailing edge piece itself. Once the rivets are set they'll probably expand to fill this space anyway, so it's not a huge deal that the holes get slightly bigger.