How to fix eaten/rotten rafter
I think your staggered-joint idea is a good one. From the look of it you'll have a solid enough base to get another decade or two from that tail.

I'd cut back just enough to get solid wood at the center, then notch the sides back to wherever you can comfortably fit the saw. Something like so:

|        |
|__    __|
|  |  |  |
|  |  |  |
|  |  |  |
|  |  |  |
|  |--|  |
|  |  |  |
|__|__|__|


Fasten the cedar or pressure-treated repair pieces with good exterior-grade adhesive and trim screws. (You can even fasten the most conspicuous side from the inside to keep the surface smooth.) Caulk against the wall, and stain or paint to seal the new wood.