What would be the required conditions for a lunar eclipse to occur only once on a precise annual basis? As I am aware, lunar eclipses can take place several times a year on Earth. However, I am curious whether it would be possible for this event to only occur once annually on a specific date (and preferably on the same face of the planet) if the moon's angular orbit around Earth were to be altered from 5°.

To put it bluntly:
How would the components causing a lunar eclipse need to be altered for a singular 'blood moon' to be able to appear reliably every year on say the 25th of September? If it is at all possible.
Additionally, would these alterations cause any other significant effects between the Earth and Moon?
A lunar eclipse occurs when a full moon occurs at the same time as a lunar node (when the moon crosses the ecliptic - the plane of the Earth's orbit around the sun)

The time between full moons is 29.53... days (although it varies slightly due to the moon's orbit not being circular) This is the synodic month. The time between nodes is 27.21... days. This is the draconic month (because of the dragon that eats the sun!) It is shorter than the time between full moons because of the curved motion of the Earth around the sun, and because the gravity of the sun distorts and rotates the orbit of the moon. 

Now on Earth, 223 synodic months is almost the same as 242 draconic months. And so an eclipse will recur every 223 months, or 6585 days.

Now you want an eclipse to recur every year. For that you would need the length of the synodic month, and the draconic month to be an exact fraction of a year. If you change the size of the orbit of the moon you will vary both the length of the synodic and draconic month. If you change the size of the Earths orbit you can change the difference between a synodic, and draconic month, but you also change the length of the year. 

So you end up with a juggling game: You have two variables to change, the Earth-Moon distance and the Sun-Earth distance. And you get three values: Synodic, Draconic month and length of a year. You aim to get both of the months an exact factor of the year. It's probably possible to achieve this, but you may end up freezing or baking the Earth. You have also changed the calendar (so "September" may not exist)

Then you need to consider the perturbations of other planets and so with time the length of the month will vary, and your three-way co-incidence will break eventually.