The CC could very well be that high from the steps because they can harbor a lot of algae, but I suspect if the steps are that bad, and it has been neglect that long there's a lot more algae in there then just what you found under the steps.
It could still take awhile for it to clear, or at least mine did. Mine was a 3 yr neglected swamp when I started on it.
So I think it will depend on what is causing it to be cloudy, is it the algae, or is there other chemicals in there that are reacting to the chlorine, are there particles floating around, etc.
What helped clear mine quicker was doing frequent vac to waste, also putting a knee high panty hose in the skimmer basket, it does the same as a skimmer sock would, and it helps trap all those little fine particles preventing them from making their way to the filter, and possible being returned through the return. Also if he has a sand filter you can add a little DE to it, and it will help trap smaller particles too.
I was also reading a thread the other day where the gentleman just could Not get his to clear (he tried everything mentioned above), but no luck.
So what he ended up having to do was actually shutting off the pump for a couple of days to allow all the tiny particles to settle to the bottom, and then did an extended vacuum to waste which removed them all with a couple of vacs a day, for like 2 days, and it completely cleared his pool. The transformation was unbelievable. Hopefully some of these suggestions will help.
His TA is zero and the pH is just showing like it is 6.