Getting rid of harsh, shrill treble

Please describe your system, including cables

It's probably the room and listener placement (sitting too near the rear wall seems to add harshness along with the bass boost).

As others have responded, changes are system dependant..
however, I had great success using a JPS Labs digital cord powering my CD player and it greatly reduced brightness and sibilance..

I agree with Tvad that more information would be helpful and I would add that harshness can also be due to, among other things, cables, plugs, dirty contacts, power line issues, RFI, interaction between your components, need for vibration control, etc. My own experience has been that it could well be a combination of a few or even many of these factors - every one of which I have experienced at one time or another myself. I would suggest an approach where you deal with these issues one at a time in order to see what helps or hurts in your system.

Your MD 308 amp is known for a balanced presentation and is probably not the source of the harshness and shrillness (unless it hasn't been broken in for long enough). Your Rega Jupiter is probably also not the problem. Per your question, switching to a tube amp could smooth the highs somewhat, but I suspect the better answer would involve a combination of different speakers and some room treatment.

Alternatively, a cheap and dirty fix would be to buy an equalizer and use it to reduce the treble energy. This is pretty sure to work, but you have to accept the compromise in signal quality that would be incurred.