Allright, with the 280's, don't bother.
But if you want to upgrade, you might aswell go for a good soundcard while you're at it.
Bang/buck, I'd still go for the ESI Juli@.
I had to thoroughly modify my Yamaha CDX-880 CD player to get anywhere close to the Juli@. It is above your budget, but it's really, REALLY good.
About the jack converter: The signal that comes out of the soundcard just isn't meant for headphones. It probably just won't play loud enough.
Tough, eh?
A friend of mine has a very nice external Tascam soundcard that was what... 80 euro's or so? It has all the out/inputs you'll ever need. I listened to it via a pair of headphones and the headphone preamp is just brilliant.
I'll look up what it is tomorrow