If you don’t have enough wires in the traveling cable, then they will have to run more, or replace the existing traveling cable. You can’t just throw a wire down the shaft. This is likely to be the reason the price is so high. There may be options if they have limited conductors left though. If they have at least two twisted pairs, you may be able to use a device to transmit Ethernet over those pairs. 2N makes devices like this. https://www.2n.com/en_US/products/intercoms/2n-2wire You’ll need a second pair for power or have to get it locally in the cab.

In addition, depending on your location, the elevator unions have absolute authority over anything done in elevators. In MA, we (the security systems contractor) can’t do ANYTHING in an elevator without a licensed elevator technician there with us. We can’t even enter the elevator machine room without them. They install all the wires, install the camera and other devices, and then watch us as we make final connections. It does make sense since we could do serious damage if we touch something we don’t know anything about. We don’t want the liability of messing with elevators either. They don’t know and don’t want to deal with the security systems work.