You're going to have rigidity problems. I would consider adding a linear actuator of some sort to the far end of the crane arm.

As for a control, you will need to do some programming to make this work. Therefore, I would be looking at an open source control platform - either Grbl (my personal choice due to familiarity with the code base) or LinuxCNC. If you choose Grbl, you will be limited in step rate if you use one of the AVR based versions; due to the requirement to do a transform for every point along a move -- so I would consider using an ARM based port, or perhaps the ESP32 based port.

https://github.com/terjeio/grblHAL
https://github.com/bdring/Grbl_Esp32

All in all, this is a non-trivial problem to solve. It's not impossible, it's just that you're going to have to dive deep into the control software to make it work.

If you want to save shop space, and stick with a more conventional machine; how about just making the rails & transport assembly tilt up for storage in a vertical position?