I'm not a pharmacologist, but I have done some research into this. AFAIUI all drugs have a measurable half-life in the body due to metabolism of the component chemicals. Broadly, there are water-soluble compounds which have a relatively short half-life (up to a few days), and insoluble compounds which typically have a much longer half-life.
The half-life (just like with radioisotopes) is the measure of the length of time for half of the compound to be eliminated. Depending upon the critical mass required to have an effect and the quantity consumed, it may take several periods of halving before the compound is out of your system.
If 72 hours gets you to where you don't feel the "dependency", it might be possible to reduce that by controlling your caffeine intake when you do drink coffee. You could try half-caff (IMO best to make your own blend, and don't skimp on the decaf part: Decaf should cost more because it costs money to decaffeinate the beans).
You could also try alternating with hot chocolate or a flavorful herbal tea (my latest fav is Yogi Teas Egyptian Licorice). A significant part may be the psychological aspect of the ritual of having a cup of hot coffee. Having a cup of hot something may just satisfy that need.