As I understand it, and I'm not an engineer, the run flats have significantly stiffer sidewalls to cope with having no air. On cars where the suspension was not designed to run such a stiff sidewall, this will have an impact on feel/tramlining etc.
I wouldn't go as far as Attak and say the car manufacturer knows best - in terms of brand - when nearly 20 years have passed since the tyres were originally specced for the Z (were they Bridgestone RE040s from the factory?) but when it comes to the manufacturer choosing non-run flat v run flat, I would personally stick with that decision (whichever brand you go for).
As above, I changed from the Bridgestone RE040s that my car came with from the PO, to Michelin MPSS and immediately noticed an elimination of tramlining and also significant improvements in both wet and dry handling. Obviously that's not really an option these days, but I'd be looking at the next nearest alternative if I was still in a Zed.