I'm lucky enough to own one of these, and it has a bit of history to it (it came from the daughter of Hacker's head of finance - it was her 18th birthday present). It also has both warrants.
It's in storage, carefully wrapped up awaiting the space to display it, so I can't power it up to check the headphone socket, but Nick's suggestion is a good one. If you're using low-impedance "buds", then that'll make things worse. Typically, a resistor of ~220 ohms between the amp and the headphone socket is used. I've just gone through all the high-res photos I took of the innards, but didn't take any of the headphone socket.
The cassette deck is made by Sanyo:
http://www.vintagecassette.com/sanyo/rd_4055
(Later versions used a different deck - the same one that Hacker used in their HCD1000 - which is made by Nacamichi. This model is slightly narrower than the one we have.)
From the pictures, my one appears to have a Shure cartridge. Sounds like your one has been changed (they use a standard 1/2" fixing).
If anyone has any service data, I'd be very interested to see it; I've yet to stumble across it. Fortunately, the unit is well-made and very modular, so fault-finding should be straightforward. I must admit that when I looked inside I was pleasantly surprised - knowing that the build quality of the radios had began a downward descent by this stage, I was expecting it to be much worse. Like earlier Sovereigns, this uses separate PCBs for the AM and FM, a decent air-spaced tuning capacitor, and lots of plugs and sockets for interconnection. In other words, internally it's more "Sovereign III" than "Sovereign IV", happily, despite the external styling being more suggestive of the later model. The push-buttons, for example, are straight from the Sovereign IV/RPC1.
Enjoy - it's a lovely bit of kit
Mark