Sciral Consistency is an easy-to-use app for tracking tasks like you describe above that have flexible intervals.
There are Android and iOS apps ($1.99) and desktop versions for Windows and Mac ($10). There is no cloud backup or sync across devices.
Take a look at http://sciral.com/consistency/ . It tells you "what's on your plate" and how you're doing in terms of keeping on top of things. And it lets you set due dates "fuzzily" instead of on a fixed date.
A downside to it is that it doesn't have any reminders apart from the color coding and the bullets in the app itself.
Maybe I'm not fully understanding how Things, OmniFocus (which I use) and the other GTD apps work. But from what I can see they all assume a task is due on a specific day. Sure, I can use recurring tasks, but that still requires me to set a task to be due on a specific date and then, if need be, postpone it. Or, as described above, I'd have to set a task to be due at its last possible date which would of course promote procrastinating on it until the last possible moment.
What I've found so far in terms of apps that do this is a Mac and iPhone app called http://sciral.com/consistency/ . It looks nice enough and seems to do exactly what I have in mind. If nobody comes up with anything better or a way to implement this in OmniFocus, I'll probably go for it.