Slide the new piece into position. Hold it in place with the forearm of your free hand as you affix the new piece to the middle ceiling rafter along your penciled line. Pic 1.

Continue to support the new piece until at least three screws firmly attach the new piece to the middle rafter.

Attach the new piece to the rafters on each side, placing the screws a little back from the edge as before and angled slightly into the rafter. Pic 2.

Anchor both sides with screws spaced evenly from corner to corner. Pic 3.

When the new piece is fully secured, remove the support piece you screwed to the wall and patch the screw holes with joint compound, if noticeable.