If you fit softer springs of any type you will be creating a new problem whilst ameliorating an existing perceived one. Then that new problem will need to be sorted which may lead to other issues.
The bare facts are that the Mini was designed with fantastic rubber cone rising rate springs to cope with road surfaces and conditions.
It is the short travel of the suspension which makes the ride seem bumpy. So if a rubber cone spring with a softer initial rate is fitted, then the rate must be higher and it must be harder towards the end of the compression to prevent the suspension hitting the bump stops. A car won't steer or have good traction with the suspension on the bump stops!
One thing which can be done is to raise the ride height a bit which allows more available travel. Then the dampers need not be quite so hard and the suspension will be slightly more compliant. It is possible to skim a bit off of the bump stops, but that can cause an issue with the hubs and is not advised.
Anti-roll-bars (anti-sway bars across the 'pond') are difficult to get right. A rear ARB is not suitable for a road car as it promotes over-steer which is fine for improving 'turn-in' under full power on the race track, but on the road it's simply unsafe.
The best option is still the original specification cones, as sold by Mini Spares and made from the original tooling, with Hi-Lo's to set the ride height and adjustable dampers to optimise the damping front to rear.
In the end, the Mini has its suspension travel limitation which cannot be overcome, only minimised.