Have been out and about in the TA (cold permitting, brrr) and the hoppity back end seems to be settling down a bit. A check through the old m.o.t. certificates shows that I've taken it as far in the past couple of days as it has been in the previous couple of years, needs a bit of driving methinks.
A few years back I had an old American pick up truck which behaved in a similar manner. I removed the rear springs and dis-assembled them, before they went back together I ground down any nasty wear ridges and the sharp ends of the leaves, a good coating of grease on re-assembly and the transformation in ride quality was huge.

The MGB rear springs are supposed to have rubber leaves between the spring steel leaves and not be lubricated in any way.

However I do find that a drop of oil every now and again does wonders for the ride quality.

From what you say I would look at the tyres - sounds like you are wearing through the hard outer bits and getting more grip - these cars certainly need to be used.

Cheers
Jeremy