It sounds like he’s being territorial outside of his room- what with the pooping and aggression. How does he act when you go into his bunny room? Has furniture been moved recently or anything else been changed (smells, food, etc)?
I assume you yelp/give a little scream and say “no” when he bites?

I wonder if any of this would help-
http://language.rabbitspeak.com/rabbittalk_anger.html

You probably already figured this out, but the turning his back on you is a sign of anger- though I wonder what’s offending him in the first place

Also, most bunnies do not like being picked up.

It sounds like a difficult situation. But hating to be picked up is the norm in adult rabbits, so I wouldn’t worry about that. It’s like an instinct, not sth they decide to do because they hate you or sth. In baby bunnies this instinct hasn’t yet developed, and that’s how it is with most animals, it’s a part of their innate survival skills.

It does sound like he’s not been “properly” neutered, he seems very sexual – drop-marking, circling you, the sudden mood-swings, the claiming of the couch etc. Here’s an article about a rabbit that produced testosterone despite being neutered: Marshal: http://rabbit.org/sex-hormones-in-altered-rabbits/ (House Rabbit Society is a trustworthy source.) This would be very rare, though.

The only other thing I can think of would be pain of some sort. How is is stomach (droppings, cecals, hay-consumption)? I suppose you would’ve noticed if he reacts badly to being touched in some certain area, which would indicate pain or tenderness in just that spot.

Imo you don’t surrender couches or beds etc to rabbits or other pets, Because if you “reward” bad behaviour by backing off, the rabbit realizes growling and lunging is the best way to get what he wants. But you will of course need some armour, like really thick gloves that goes high up on the arms when you refuse to let him bully you off the couch. And no violence from you, just firmness and stubborness.

Please keep us posted, I hope you’ll get many more answers and suggestions here.

Like Bam, I wonder if there were complications with the neuter. Especially since the onset of aggression happened directly after. Had he been to the vet prior to his neuter?

I suppose even a subtle spine or neck misalignment due to the way he was positioned might cause some chronic discomfort. The only outward sign being aggression.

If not a health issue, then you’re probably dealing with a learnt behaviour. What do you do when he bites?

Gorgeous bunny btw. Love the big brown eyes!