Ok, we're finished the repair! I forgot to take pics of the threaded rods/pins we epoxied in place, but we did definitely do that (x4 of them, 3" into the existing concrete, 2"+ each for the new concrete). The piece of wood was perpendicular to the front of the step (the face), so we chiseled it out completely (it was sopping wet!), and then put some dense styrofoam panels loosely placed in the void left by the removed wood piece. This was because it would have been hard to get a good pack of the new concrete back in that area, so the styrofoam will fill the area without expanding much, and since it's got a tiny bit of room to play with, it shouldn't put any force on the concrete. We also put a small plastic tube (thick, strong) for drainage from that area, down below grade to the gravel below the paving stones.
Here's the top view of the mold (we used the same dense styrofoam for the kickplate area (?) and then a lightly-oiled 2x board for the end of the nose.
Here's the finished product:
I will probably grout or caulk the very edges of the vertical patch to give it a bit better look, but overall it should be plenty strong, and isn't too noticeable (and once it's a bit dirty it should blend right in, hahaha!).
Oh, and I plan to cut the expansion joints next time I have a few moments.
Thanks everyone for your insight and help with this... saved me a lot of money!