Yes, whatever cheese you make, you may age at commercial cheddar temps, or higher at continental cheese temps. There's nothing extremely unique about cheddar that makes its aging process drastically different.
You can eat at any time you want. Of course, the flavor will change over time.
If you want to make a cheddar and use a cheddaring process, then do that. If not, then create your own cheese.
George, a more moist cheese has a shorter shelf life and tends to be at optimum flavor for a shorter period of time. And yes, it does age faster.