So basically, I think I've really dun goofed here.
After much debate, I finally decided to exchange my old 3DS with the 3DS XL and in my excitement, I didn't actually read up on the fact that if you want to keep your old games from console to console, you need to do a system transfer. To be fair, the store I traded my game in didn't mention this, but I'll try not to place the blame on anyone but myself. Not only have I lost my old games and save, but my account activity with all my ambassador program stuff as well as any eShop games. I'm not asking if there's a way to do it with my old console or a SD card but if there's a way to link to my old account, some settings option I'm not noticing or if I've truly messed up here, I may not have been terribly clear here so I'm more than willing to clarify any point. I've contacted Nintendo support but no response yet.
UPDATE #1: Just contacted Nintendo via telephone and they said there is NO way to do it other than system transfer, so rush to the store it is, not holding much hope though. I even mentioned the rumoured Club Nintendo way of getting it back but they seemed bemused by the idea and said it's more of a rewards scheme or something along those lines than an actual record of games owned.
UPDATE #2: Just went to the store and they said they wiped it, by the sounds of things, pretty much as soon as they got it. Sigh. Think I'll let off some steam by writing a very disappointed email to Nintendo about it. How British of me. Either way, hopefully this has enlightened people at least to make sure they do the system transfer before trading in.
UPDATE #3: Sorry to drag this out even more, but it looks as though my response to my email to Nintendo support actually had a very interesting paragraph:
Please note that formatting the console does not delete your eShop account and download content unless you have created a NNID, providing the retailer has not manually deleted the eShop account your purchases may still be on the console.
So even though the games themselves are gone, the games are still registered to the console in the same vein as Steam. After reading this I headed to the store, asked if I could see my console's eShop Account Activity and (after a 10 minute system update) my past purchases were all there (including my credit card information which is just a bit frightening) so I tried performing a system transfer old for my 3DS XL to rebuff me saying my battery was too low. Seriously. I'm heading there first thing tomorrow and I'll let you all know if this really does resolve everything.
UPDATE #4: Went back in the store today after waiting ~20 minutes for the system transfer, all my previous account activity is now on my new 3DS, happy days! So I guess as long as the store has your old console in, you can prove you traded it in (should the store need to prove it anyways) and they haven't gone as far as to manually delete eShop contents, you can still recover your downloadable games.
Best Answer
Unfortunately, as you have noted, without the original system to transfer to, you are likely without hope. 3DS titles are tied to console, not to any ID (Nintendo Network ID or otherwise), so without the console, you can't do a whole bunch. If you had the console, you'd be able to do things differently, but as it stands, there isn't much you can do.
There are stories online where people say you can contact Nintendo to get your stuff back, but since Nintendo themselves seem pretty hush on the matter (their website states that you can only do things through transfer), I don't know how lucky you will be. Club Nintendo keeps a sort of record, in a way, so they might be able to help that way.
I would also keep in mind that stores usually wipe any used consoles they receive, so even if you can get to the store, it is not necessarily true that you can even get your stuff back, even if they have your particular console still, as doing a format wipe of the SD card and the system means that your information will also be gone. This prevents the next owner from being able to essentially get free games by downloading what you had already purchased.