I hear a lot of nuclear options being tossed around, but I disagree.
Costumes can be adjusted and refitted to size. They can also be sold as-is for a bit cheaper (say half to 75% what it could make, depending on the work involved.)
I think your bf has a real talent in how much effort and motivation he is able to pour in to these costumes. That same energy can be redirected to modifying costumes, but it would be a huge request to ask him to handle the entire selling process on his own.
I think, if you do a bit of the talking and encouragement, you can get the process rolling on selling the costumes. If the bf can agree that you put forward the effort try to put them up for sale, that might be the push he needs to accept actually parting with them. A lot of times, people can just be overwhelmed by the amount of work, unknown number of steps that might be involved to tackle a large project like this. So you might have to do a lot of the business work side of it, and then keep him involved as things get rolling.
Selling the costumes involves a good bit of work on its own:
Pictures - not just the costume in a box, but modeled on someone, ideally posed. Plain, or even better, a creative background can really help make the costume pop and seem appealing. Some of his friends might be able to help out for modeling, even for free. You dress up in character, you like the attention, bonus in that they already know how to pose for it :D
Description - Itemized list of the complete costume that will be shipped. Sizing, determine how much work it would take to modify. Sometimes buyers might request for a size change, which would involve their measurements, and the bf determining how much effort it would take to rework the costume to make it work. Some things might be too much work, other things you might even charge a little bit more for modifications, or do small mods for free.
Price - Determine generally about how much it would cost, and how much it might go for. Naturally a more recent or character that's popular again (think X-men movie just came out = lots more X-men costumes, or new Zelda game is out = people are on the lookout for retro Zelda costumes) might be higher priority to put up for sale than an obscure or generic game character
Organization - Bunch of costumes stuffed in boxes will end up being a nightmare trying to find costume X and prep it for shipping / figure out modding it. Sorting, organizing, maybe pre-wrapping the costumes will help a lot in keeping things organized. The lack of space is a real cap here because there's less room available for prepping, displaying, packing and keeping these separate. Also, a lot of times when customers contact you asking questions, they'll refer stupid vaguely to a costume and assume you know what they mean ("Oh I had a question about the Mario costume" "I have 4 different costumes, but they were all Zelda, which one were they referring to?"). Just part of the territory, it's helpful to know how to talk to customers to super clarify exactly what they want and not just what they're saying.
Sale contact: your bf might be too emotionally invested to talk about selling the costume with a stranger. This requires a little bit of work, a little bit of salesmanship. Sometimes customers have concerns, sometimes they want to negotiate on price. They might want resizing, but don't know their own measurements or how to take them, It can be a lot of work, and you'll be working with the bf on what is possible or not.
Customer relations: After sale, people will call back with questions, requests, they might have measured wrong, they might not like what they got. Some things you might be able to negotiate, other things you can say that the sale is final and won't accept a return. Other times a costume might get damaged with use and you can charge separate for repair (additional side business). Sometimes people will damage the costume and expect you to send them replacement pieces, like, what?
So.. that was a long type up. Nothing is 'unmodifiable', but it can be a good deal of work to sell them with any amount of success. It's not simple or easy, but a good team working together and communicating well can tackle even this. Now, the real question is, are any of these costumes any good, and how much would people pay for it?
You will eventually hit costumes that don't sell even after being posted a long time, have no appeal, and no chance of being popular again. Have some cutoff point for tossing these out and removing the listing. At the same time, some things will be up forever and then sell suddenly for no reason. It just took the right person seeing the listing, or finally getting enough money together to go through with the buy.
Sometimes you can tweak the listing, other times it's completely random. This is where running a business of making costumes completely differs from a business of selling off inventory. You already have a product that might or might not be appealing.
A costume making business, people usually have an idea in mind and the costume maker will go about putting it all together. There is some overlap, but you can charge way more to put a costume together for a person, selling a pre-made costume is more of a chance / luck thing that the viewer likes it.
Post write-up idea: A lot of conventions often have seller booths. Might it be possible to rent a space and try to sell costumes? This can have varying success, especially depending on the convention size, theme, interest. You'll still need a lot of time spent prepping, packing, and getting picture and description of the costume. The more professional you can make the booth seem, the better you can charge for the costumes (think costume business, and not garage sale "dig through a box"!).
Good luck!