The DAC inside your DAD3 is the Philips TDA1305, which is a pretty open and natural sounding chip. I’ve known a couple of people who have used it, who migrated over to the ESS Sabre 32 DAC in the Audiolab 8200CD, and they seem very happy with its performance. So if you’re looking for a modern equivalent, that would probably be it. However, it’s always worth auditioning for yourself.
I don’t know if you can pick up something similar sounding for £500, but I’m sure the other people here will have suggestions.