any AirPort Extreme with a hard drive attached functions just like a Time Capsule
Not quite. Even if you use the current version of the AirPort Extreme......which is the only version that Apple officially supports for Time Machine backups.......you may have forgotten that the AirPort Extreme USB port is old and slow USB 2.0.....and....that the processor inside the AirPort Extreme further limits the speed of data going to the USB drive to about one-half of normal USB 2.0 speeds. Not too impressive.
So, while the AirPort Extreme / USB Drive setup might function "just like a Time Capsule", it will do so at about half the speed of backups that go directly to the drive on a Time Capsule.
A variant....and better choice......of Option 2 would be to add a USB drive to the Time Capsule and use the Archive function in AirPort Utility to copy all of the data on the Time Capsule drive over to the USB drive. Then, erase the Time Capsule drive and start over again with a new backup. This is a more complicated process, but it is a better performance option.....if performance is important to you.