Hello. I am in the process of doing some minor upgrades to my new (

) 1993 MX-5 LE. The tyres currently fitted are Simex 205/45 ZR16 with a relatively nice set of mags. The ride is very firm and you feel every bump, but the consolation is that it corners very nicely. As the rubber is getting really low, I want to replace them but would like some advice on how I might improve the ride on the open road. Currently, you feel every single bump. There is a bit of vibration, which my mechanic said is due to a slight flat spot on tyre (possibly on the rim as well, we have not separated tyre from rim), plus he said alignment and balance are probably out a little. Regardless, he recommended a softer tyre and possibly a size change. He took a god look at the suspension and said that everything seems to be fine, so he was more inclined to feel the rough ride was coming from the wheels.
Can anyone please provide a recommendation to help improve ride comfort (especially soaking up the bumps a little better), without overly compromising cornering etc? I don't want to go so passenger oriented that I lose the sports car feel, so if I have no choice, I would err on the side of handling over comfort.
I appreciate any feedback.