Turned out pretty well. Read on for details and other problems.
To make a long story short, when I bought this house the driveway had sunken 4 inches (as had the sidewalk). This past summer I had the driveway leveled using magical foam injected under it (skeptical but it’s got a 5-year warranty so we’ll see). This left the sidewalk considerably lower than the driveway, the bottom of which was now to the top of the sidewalk.
As a solution to this I broke out part of the sidewalk today and formed it up to be level with the driveway. 12.5 80-lb bags of concrete (and a borrowed mixer) later it’s as shown above. There’s still a step, but it’s in a more reasonable spot. It wasn’t worth doing the whole thing for the reason below:
Here’s the kicker - the footer of the porch also sank down several inches in the 40-ish years since the house was built. I very recently discovered that the concrete slab on top isn’t even sitting on the foundation at that corner (previous owners spread mortar over the brick, which can be seen to be cracking because duh) but rather being supported by the tensile strength of the rest of the slab (!). So that will probably crack/drop at some point.
There’s a good chance that to fix it the entire porch (I’d say 7x16' without actually knowing the measurements) is going to need dismantled, a new footer poured, brick laid, top slab poured, etc. I’ve classified this as a “next year problem” though. Not looking forward to that, cost-wise.