He's territorial marking his litter area. It's possible the neuter could help fix that, but there's also a chance it won't as it's something even fixed rabbits will do. And especially since you have other pets around. He's letting them know those are his spots.
If the neuter doesn't resolve the behavior, one thing you could try is spraying the area down with vinegar/water mix, natures miracle, or other pet safe scent neutralizer, to neutralize the scent that's been left behind. You don't want to clean the scent off his litter box though, you want his scent to remain on that so it's established that area is clearly his. Though there is a chance this could just set off him marking the area even more. You never know with rabbits.
I don't know if this is something that would work, but you could try one of those rubberized cat litter mats with the rubber nibs on them that prevent litter tracking when the cat steps out of the litter box. As long as it doesn't become a chew hazard for him, he may dislike the feel of it on his feet enough that he won't want to poop mark there anymore. Plus it would cover up the area there that has his scent on it already. Might be worth a try. A lot of things for deterring unwanted behavior, is a matter of trial and error. I've had to try out all sorts of different set ups to find the right one for each particular rabbit, as they don't always respond the same way to things.
Honestly though, he's doing pretty good for an intact male. I have fixed rabbits that aren't as tidy as he is.