Yes. Cutting to the chase, I did it. Just a few minutes ago, I was finally able to muster the will to do 100 consecutive push ups. Upon completion, I collapsed to the floor!
After failing in my first attempt at the 100, I repeated weeks 5 and 6 of the hundred pushups program. This time, I was able to perform those sets better than the first go round. And after finishing up the final day of week 6, I rested for two days before attempting the 100 consecutive.
Push ups are a great exercise. They have really helped improve my upper body strength. And, hopefully, the lack of lower body stress gave my injured knee the help it needs to recover. Anyway, now I can stop obsessing about push ups and get back into a more diverse training regimen.