Giving him a few extra litter boxes for now, may help. If he is picking specific areas to pee, then place the litter boxes there.
That's good that it isn't parasites. Well formed cecotropes aren't really going to stick to the fur for the most part. Usually the problem is too many carbs and sugars in the diet, causing a bacterial imbalance in the rabbits digestive system, resulting in mushy poo, that then sticks to their fur. To correct this, if he is getting treats or veggies, he's a little young to be having those yet, so it would be best to stop those to see if the mushy poop clears up. If it does clear up after eliminating these, or you don't feed these to him yet, then the next step is to reduce his pellet amount a little bit, and continue to offer unlimited (preferably)grass hay. If after a couple days he is still having soft poop, then reduce the pellet amount a little bit more. If the kind of pellets you are feeding, happen to be the kind with 'treat' pieces in it, then that can be the reason for the mushy poop because of all the extra carbs. So you would want to transition slowly to a plain alfalfa based pellet. It is pretty important to try and figure this out though, because if the mushy poop continues, the digestive system will get progressively worse, and then you could end up with other health problems like GI stasis and a blockage, which is pretty serious. But it's almost always treats, new veggies, or too many pellets, that causes mushy poop in rabbits