I tried a quick-set mix last year on a 1/2-1" crack, with closed-cell foam wedged deep into the crack. The "repair" cracked while drying but was good enough to keep most water out over the winter, so the crack didn't really get worse. We lived with it this summer, and I may just cover the crack with rubber over the winter and plan to replace next spring. The concrete guys around here are not interested in a small job of replacing 1-2 sections of an existing apron.
I plan to do some testing to get the mixture/texture right before trying to replace the entire section. Ours has a very pronounced swirling brush pattern to aid traction that will take some practice to replicate.