I suspect this can be replaced with a suitable foam-like liner, but I'm not sure how feasible it is to do this without extensive disassembly of the mirror box and its contents.
Btw...I have a soft spot for the Mamiya Z system. My very first SLR was a Mamiya ZE. Many years later, I got a ZM, which I used extensively for a couple of years, until it started to develop issues.
Meknes, Morocco; 2016. Kodak TMY2. One of the last images I made with the ZM.
Sorry for barging in without offering much help. I hope you'll enjoy your ZE-X for a long time to come. It was the flagship of the Z-series.