I totally agree that if there is a poopy bum problem, then it might be from the veggies. I see that you're in another country, so I assume that you have a hard time finding good quality pellets. Do you have to get the stuff with the corn and the different things in the with the pellets?
BUT I only suggest doing this, if your bunnies can handle the greens. If there is a poopy bum problem, then put them on a hay and pellet diet for a few days to see if that helps. If it does help, then re-introduce the greens one by one and slowly so you can rule out what is making their poop soft. If its most of what you feed them for greens, then you shouldn't take them off pellets; you should give them more hay.
As for a no pellet diet, you have to give a lot of variety in greens and hay. The rabbit that I had that was on a no pellet diet, got about 4-6 cups of greens a day, all mixed. Then she got about 5 times her body size worth of mixed hay in a day. She ate all of that. She maintained a really good weight. I only gave her fruit once a day and it was always the same.
On a daily basis, she got cilantro, red leaf lettuce, green leaf lettuce, romaine lettuce. She got parsley 3 times a week one week, then the next week, she got a spring mix salad that had a bunch of different things in it, things that were higher in calcium, 3 times a week.
You have to watch out for things that are high in calcium or oxalates. Just make sure there is enough variety.
I also gave her like 3-4 different hays a day, all mixed together. She really enjoyed her hay.