I've never had "dreaded buzzing" problems with my concert lead. Sure I realize you are talking about a concert bass... but there really ain't much difference than the reverb I have but don't use on one channel.
The volume fluctuations are probably caused by a bad volume control. I have seen a lot of this happening on these amps, plus the possibility of the bass control being bad... also causing volume fluctuations. My volume control was so bad that I could push on it to get the volume back, but when I let off the pressure, the volume loss came back.
If you want to shield the wood enclosure, then you could use a metal screen, copper foil or even aluminum foil (the kitchen kind). Staple it to the inside of the wood... but it will only work effectively as a shield if it is grounded. A small wood screw into the wood, with a large washer making contact with the shield, and a wire from that to some existing screw on the chassis should handle that.
But it bothers me... I wouldn't consider any member of the concert series a "great antenna"... certainly not by the nature of it's design. Since most of these amps are probably in the 25+ year old range... the age of the amp, and most likely the dirt and various accumulations over the years are the culprit. If your cables are good, and you are using a good grounded three prong outlet, then you might want to apply some contact cleaner to the input jacks, even replacing them if they are so badly worn.
Sometimes, the input jacks get loose. Before they are tightened, sometimes dirt can get between the jack and the chassis. Over time, this dirt can build up to prevent a good electrical connection between the jack body and the chassis. What should be ground... the inside of the jack that connects with the cable may now be at a level above ground. This can cause some strange sounds to result. At the least, take off the nut holding the jack to the chassis and clean behind it.
Hope this helps!!
Joe