I'm actually quite surprised to see no real water damage under the part you've removed. My experience with manufactured marble showers is that they're guaranteed to leak waaaay before their 35th year. Usually first at the drain as I've not seen an adequate waterproof method of attaching the drain to the floor in those showers. All of mine have been over concrete SOG, fortunately. Your application would make me very uncomfortable.
But you didn't stop by to determine my comfort level, did you now?
I've never seen that plastic molding you have. And I'm not seeing a good way for you to replace it if you did have a new one. Do you know if they used something similar at the wall/floor junctions? Just difficult for me to grasp a caulked joint in an assembly like that remaining waterproof for 35 years.
My opinion; worth price charged.