How long does reverse DNS take to propagate?

This is nothing to do with the mythical idea of "DNS propagation". As Zoredache has quite rightly said, this is an erroneous concept (based, if it is based upon anything at all, upon the long-since-altered behaviour of some domain name registries). The DNS does not work that way. Your data were available from your content DNS servers to the world as soon as you entered them.

This is everything to do with the fact that you have name→address conflated with address→name. You've entered a name→address mapping but you've expected that to magically affect the lookup of an address→name mapping. You're spending days at a time waiting for things to "propagate" when you haven't in fact enacted any changes to the relevant data in the first place.

If you want to look up the new name→address mapping that you've just entered, look up the domain name. If you want to change what an address→name lookup returns, change the address→name mapping data in your database. Address→name mappings do not involve either A or AAAA resource record sets.