I'm assuming that in addition to runflat tyres, you have the sports suspension option as well - it seems to be the combination of sports suspension and 17" runflats that really make people suffer.
If so, the 'nuclear' option would be to change your car to standard suspension by swapping out all four dampers. These cost Ł440 at full dealer prices and then there's the labour to change them, but that would keep you on OEM MIni parts and so not void your warranty. You might be able to get your dealer to pressurise Mini into making a contribution.
This sounds a dramatic/expensive solution, but four new tyres isn't going to be all that much cheaper.
If you have standard suspension with 17" runflats, then changing the tyres would help a bit. My experience is that changing 16" runflats to 16" non-runflats doesn't make a huge difference.