Seems to me I recall reading about some people writing to them and successfully requesting to buy some things that weren't in the store anymore. If anybody knows about this, I would love to know who/where to write in order to do this. Thanks.
This is not an officially supported and guaranteed method, but yes occasionally you can get lucky. You can submit a politely worded Support Ticket telling them that you would really like to buy a no-longer-available item. If Customer Service approves your request, they may sell it to you even if it's no longer available.
They allowed one of my guilds' leaders to buy an old house this way, and I was able to buy an old furniture pack, but they said no to an old costume. So go ahead and ask, trying doesn't hurt, maybe it will work for you!
Items that are in any past/present/future Crown Crates (or likely/able to be in crates at some point like costumes, mounts, and etc) are a "no" as far as I know. Anything else is case-by-case.
Since crates don't contain limited houses or limited furnishing packs, requests to purchase those at least have a better chance to be granted. I don't know how likely it is now that those items can occasionally come back in the store, though.
(If you are wanting to purchase a house through support, be aware that they can only grant a completely empty, zero-furnishing version, not the usual unfurnished/furnished versions.)
Ultimately, just be very patient and polite when you ask!
(Note that most Support Tickets initially get a canned response that needs to be replied to or else the ticket will be closed after some time due to no reply. Just politely restate your request and go from there.)