Part of this is caused by the direction of engine rotation, illustrated when you blip the throttle when stationary.
If the engine rotates anticlockwise from the drivers seat, the resultant force on the car will be clockwise, so it will bear down on the offside rear. So hard acceleration will put more load on the offside than the nearside. Then you can add the weight of the driver. Leaf springs do sag. In an ideal world they would be of a material which resisted flattening, but cost dictates something below that standard. There is no pure engineering fix for this except replacement, although you could lower the nearside with a spacer as a short term solution. I wonder if Morgan have considered a single leaf parabolic spring upgrade. This is available for MGB's but with mixed reviews on longevity. Additional springing could be applied by a coilover set up on the rear dampers. It would need anti tramp as well on both sides.It's the sort of thing which could be done 'at home', as is the spacer plates on the bottom of the cross tubes. Maybe when I retire and have more time......