Unfortunately, your experience is fairly common. All the food from the day is ready to exit during the nighttime hours. Also, any inflammation or upset in your j-pouch due to healing or imbalance in your gut flora will be exacerbated at night. Meaning: you have excess gas and stool and can't sleep for very long.
I really hated hearing it would just take time, but as you have seen during the day - it will get better. See if probiotics help you out any (ease into them - immediately more is not better). And give it time. My experience was much like yours. I was up all night until about 4:30 am - and then there wasn't much night left to sleep.
Also - something to try if your doc is okay with it: try taking a Prilosec daily. Reducing the acidity in your system may help. There is a study or two that show an 80% reduction in pouch inflammation / symptoms after takedown when taking a PPI like Prilosec. Apparently it not only reduces the acidity but also changes the bacterial composition of your gut because of the PH change. Worth a try.
Steve