I think you're mistaken While the Eibachs are close to stock height, I am certain they lower the car somewhat. At the same time, like all aftermarket springs, they are a higher rate spring - meaning that they're 'stiffer' or 'firmer', partly in order to avoid exactly what you're seeing: bottoming out. You'll find the M3 springs to be much the same. Lower and firmer, but still susceptible to bottoming. Your best bet is to get stock springs again. Even then, there's no guarantee you won't bottom out (depends on loading and your local driving conditions), but I think it would probably help.
For my 1994 325i Convertible: I bottom out over bumps with my stock height Eibach replacement springs. I understand that I cannot use the springs for a coupe or sedan due to the greater weight. Could I use springs from 1995 M3? Would they be firm enough to handle the weight?