The first really good Meg was the Phase 2 cup I think, but if you have lowering springs, I suspect they might be the main cause of your handling woes. I’ll spare you the details why.
Short of coilovers, there’s very little aftermarket suspension stuff available for the Meg 2. I reckon you’d achieve just about the best road handling possible by finding a Phase 2 Cup at a wreckers and transferring all of the suspension over including the rear beam. Some adjustable top mounts might then be the icing on the cake.
Failing this, get some good tyres, accept the car’s limitations and enjoy.
An LSD conversion would be good but very expensive and secondary to suspension IMO