I would tell my DH to rent a storage unit. Yes, he will probably freak out at the expense, but...you can show him the bill for weekly marital counseling and it might seem tame by comparison.
Are you wishing to have more space for your own things? If his stuff is contained in closets and in one trunk, I honestly think that is probably okay. He just has half a closet more space than everyone else, which in the large scheme of things doesn't seem like that big to me, esp. for someone who has hoarding tendancies.
So I'm guessing that he also has a ton of stuff everywhere besides those storage areas, which is where I think the storage unit comes in handy. He can store whatever he likes at the house in "his space" but anything beyond that must go to the unit. No matter what, you guys are "paying" to have that stuff in your face, with fighting and agitation. When it's out of your hair, you need to let it go, and let him deal with it, when he gets tired of paying the $50-100/mo for the space he will deal with it. It will buy no more nagging or frustration or him having to worry that you will purge his stuff.
My DH is not a hoarder, but he is really lazy about doing dump runs and going through old stuff even when I have almost gotten down on my knees and begged him to. Finally I had to tell him that I was going to hire the 1800 junk guys if our own personal laundry room dump was not hauled to the dump like I'd been asking for the last 6 months (I don't have the time to do it myself, and even if I did, I couldn't lift all the stuff and take care of it at the time due to health issues). Strangely enough, when faced with paying the extra $100 he magically found the motivation to do so.
It wasn't a threat or said nastily, I just explained that I was tired of fighting about it and feeling pissed at him all the time, if he didn't want to do it no big deal but I needed that crap GONE and so I had a plan in place, unless he told me beforehand to move up the time and go ahead and call them.
I did the same for the self-storage and my ex's stuff. I didn't want to have to go through it all, didn't want to have him get all pissy at me for throwing some important wrapper away or something, so I told him I was renting a storage unit, everything not put away in drawers and in closets was going there (it was very close by, which was a plus) so that we wouldn't fight about it any more. He actually did prioritized what he wanted in his drawers and closests (dumped the rest on the floor), and on moving day I moved all that stuff to the unit while he was at work, and when the bill for it came I put it on his desk and did not even open it. He was happier with all that stuff gone too. Eventually he did go through the unit stuff and we were able to get rid of the unit after a year. And again, it was not penalizing or anything. We had actually been going to counseling and paying $75 a session for weekly sessions, which is why when I told him I noticed we were mostly fighting about Stuff, and why didn't we try spending a quarter of that on a storage unit, he was game.