I need to repair some rotten 5"x3.5" (actual size) rafters (the one in the pic is the worst). I'm thinking about using a pair of unequal length 2x6s to create a sort of half-lap joint with the cut-back timber, and adding a trim board. Is there a better way? How do I make clean, square cuts to the 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:
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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.
How do I make clean, square cuts to the rafter (tail)?
You may want to try to gently insert shims to add a little extra space between the rafter and the 1x4 roof boards. I would use a circular saw to start; you will not be able to cut all the way through (5") with a common circular saw, but it will give you a clean cut through a few inches. You'll need to use a reciprocating saw (and care) to finish the cut. You might be able to wrap the tip of the saw blade with tape to help prevent damaging the roof boards. Alternatively, an oscillating (bare) tool might be helpful.
Is there a better way?
It would be ideal to remove and maybe replace the 1x4 roof (above the rafter), but I suppose that this house doen't need a new roof any time soon? The most expensive but obvious solution would be to replace the rafter(s).
I would use a combination of approaches for this. To cut away the rotten wood I would use a small door jamb saw. It's handle is offset - it will make working in that space easier.
You probably won't be left with much good wood. To shore up the rotten wood, I would inject epoxy. The West system is ideal for this. It's not cheap, but it's cheaper than taking the roof off.
The West system is designed for wooden boat repairs - that should make it a good fit for this application.