Why 10? it seems to me that the fall of civilisation would be fertile ground for many of the existing religions to fragment even further, new ones to be created and there would also be people without a religious belief both atheistic and agnostic. If you wanted a commandment belief system that could be added to all of the above to encourage cooperation between newly meeting groups after a fall who don't share all of the same beliefs. You would have to distil down a set of commandments that are unlikely to directly conflict with the existing ones of a basically civilised society but would show those in that same society that you are basically civilised even if you don't share all the same beliefs. It just so happens I have on occasion thought about this kind of thing and in Blue Peter fashion here is one I prepared earlier
I came up with it in one of my earlier failed attempts to make the world a better place a sort of mildly humorous fictional religion/moral philosophy a bit like the spaghetti monster one but more going for the laugh with rather than laugh at approach.
Name of religion/moral philosophy :- HARPE
Church of the “Happy Accidental Recursive Paradox of Existence”
Corner stone rules for HARPE
1. We should not steal .
2. We should do unto others as we would have done to us .
3. We should try to understand the Universe around us .
4. We should know that there are always exceptions to rules .
 As well as property do not take life, health, respect, etc.
 Consider the views of the others when implementing this.
 Helping and asking for help in this quest is allowed and encouraged.
 Try not to be too selfish when choosing those exceptions and think about the consequences of actions taken. As the guy in the movie said "Nobody's perfect" but we have yet to meet the entity “Nobody's”.
The paradox of existence and why we can be a Schroedinger cat religion slash moral philosophy for those of faith and atheists alike is that the only common tool that believers and non-believers have is that of logic, as the non-believers don't also have the faith module but those of reasonable religions are allowed to ask logical though possibly awkward questions.
As the Japanese proverb goes if all you have is a hammer everything looks like a nail.
So when asking the four big questions “Who? What? When? and Why?” with logic being our metaphorical hammer you soon realise it is also the metaphorical nail bent into a round shape as the big questions tend towards circular logic if you go far enough.
If you believe a God created the universe then what created that God? Or if you believe some weird quantum fluctuation in nothingness created the universe what created that fluctuation?
When logic is circular it is a paradox that holds it in that shape: chicken then egg, or egg then chicken? A circular paradox logically has to be accidental for if it were deliberate it would have a cause and not be circular. And if you have got past “I think therefore I am” then logically you might as well try to be happy.