I suffer from this from time to time as well..
My wife just got me a squatty potty for Christmas so I've only used it for 2 weeks but it does seem to help me feel more "empty". Another great tip is once I go, I stand up for about 10 seconds, sometimes put some light pressure on my lower abdomen with my hand, and then sit back down. It usually results a little bit more coming out.
I also started talking Visbiome probiotics and I've noticed a huge decrease in the gas I have daily. Unfortunately they are expensive but they help. They are designed specifically for IBS/J-Pouch. If you go down this route, just a heads up you might have some increased gas for a few days while your gut re-balances. 3 packets of the regular strength packets seems to be my magic number.
You can also experiment with using a fiber supplement such as Metamucil. It will help bulk the stool up and things tend to come out much smoother.
As you mentioned, diet is probably the biggest key of all. It will take some time and will power but it plays a huge role. I was stubborn and it took me years to finally accept that certain foods just aren't worth it anymore. Sugar, diary and heavier beer trigger that "explosive" feeling you are talking about for me. I'm feeling pretty good I cheat and have a couple light beers from time to time.
You'll come to find out that every J-Pouch is different and it takes some personal experimenting to find out what works best for you.