There is only one way I found that (seems) to work.
(And it is a bit complex and requires access to a computer each time you want to play after something else)
After playing PH, you stop and switch to another game, it saves the EEPROM and overwrites it with the new game.
If you then don't load up PH 'till you get to a computer then you can continue playing other games, if you load up PH and it says 'creating new save file(s)' DON'T load up your DSX or it will save the dud data over your data.
Now the complex bit :|
Connect to the computer, and copy your zelda save to your computer.
Load up zelda on your DSX and start a new file (or anything that makes a save), turn off and turn on again letting it save the EEPROM data.
Don't bother loading up a game, just turn off and plug back into the computer.
Now replace the save on your DSX (now dud) with the one you backed up earlier and start PH.
It may say that it is partially corrupted but SHOULD work.
I have used this three times with success
Explanation: I think for some reason the DSX needs a zelda save in the EEPROM to load properly... If you play any other game it overwrites this and so it doesn't work.