You did not mention if it is your normal habit to stay up until 1am and sleep in until 8am of if you only do this during a liver flush.
Consider the human body's circadian rhythms. According to ayurveda, 10pm to 2am is Pitta time. The liver does much of its work during this time and cleanses itself between midnight and 2am. You need to be in a deep sleep for this cleansing to occur properly. Flushing the stones out is great, but the liver needs to regenerate and repair itself too. If you are in the habit of staying up late, you compromise your liver's activities.
Melatonin production is also important for the body to repair itself. The pineal gland in your head will start releasing melatonin ~9:30pm in an attempt to make you go to bed and be asleep by 10pm. The melatonin levels are designed to rise after that point to keep you asleep and help with the body's nightly repair and maintenance. Any light hitting your eyes after 10pm with decrease your melatonin levels and inhibit your body's repair mechanisms (eg, wreak havoc with your hormones). We are designed to sleep when it is dark (and sleep in the dark)and awake when the light returns.
We are designed to empty our bowels and bladder shortly after the sunrises. If we continue to sleep past sunrise without eliminating, our bodies start reabsorbing the toxins that we are supposed to be expelling.
Please consider that coffee is acidifying to the body and aggravates the liver and kidneys and helps create more stones. It is also dehydrating, so you'll need to drink more water. Coffee and Epsom Salts on the same day may be overly drying.
It is good that you are taking steps toward better health by flushing your liver.
Hopefully you will begin to support your health in other ways. Everyone needs to start where they are. Congratulations for starting.