I figured out a rather simple method to saving your world after you die on hardcore, and will allow for you too switch to regular survival or creative if you need to. This is intended toward the preservation of a Hardcore mode world for bragging, or if you just want to keep playing, and not necessarily on hardcore mode anymore.
Here's how to do it:
1. After you die, do not hit the "Delete World" button, you need to just close Minecraft. If you do happen to accidentally hit the "Delete World" button you will not be able restore it with this method, I will explain a method on how to do that after.
2. Go to http://mc.42nex.us/ and get your seed of your hardcore world, you may want to write this down.
3. Start a new Hardcore/Survival/Creative world, the option you choose here will be the way your Hardcore world will be after restoration, and use the seed to your hardcore mode world, and create the world.
4. If your spawn point is not the same as your Hardcore mode world then you may want to change it with a program like lolEdit or MCEdit
5. After your spawn has been changed (if needed), then open up your saves folder (start>run>"%appdata%\.minecraft\saves") and locate your old Hardcore mode world and the world you just created.
6. Copy the "level.dat" and "level.dat_old" files from the new world to the old Hardcore mode world, you may want to back-up the files before overwriting them though.
7. Log in to Minecraft and open up your old Hardcore mode world and you should be back at spawn with nothing, just as if you died in Survival.
If you already hit the delete world button you may be able to find a Windows-made backup of it, right-click on your saves folder, hit properties, then go to Previous Versions and choose the newest version that was before you died, then click open. You should find your Hardcore world in there and copy it over to the saves folder. This will restore a previous version of your world, you may lose some stuff, but you should keep most of the major stuff, and as far as I know this only works with Windows.
This is not really intended to save yourself after you die, its more so that if you do die and want to show-off your world (brag about how much you got done in hardcore mode) you have the ability to, and there are numerous people who may feel that they shouldn't have died, or a new player to the game didn't really understand hardcore and doesn't want to start from scratch again.
Regardless of the stated reasons, there still seems to be something a bit screwy about deliberately picking a way of playing where the biggest, most defining feature of that way of playing is that the world gets deleted when you die and then finding a way to work around that big, defining feature. :/
You know, you could play on survival and just delete your worlds yourself when you die but if there was one really nice one that you wanted to brag about you could simply not delete it. It strikes me as there are quite a few people playing "hardcore" because they like the idea of playing a mode that is so "bad ass" but they don't actually want to have to deal with the features of that type of play.