First let me say I have no clue about crypto currency. But after reading this thread and having a general understanding of the setup here is what I would do.
Use buildroot to create a custom linux kernel, much like FOG’s FOS operating system. If one was ingenious, they could reverse engineer FOS and then possibly load the program needed for the crypto mining into the init.zx and also reconfigure the master fog script in FOS to call the crypto mining program. FOS boots and runs out of memory, no hard drive is needed.
Now the cleaner way would be to use buildroot to create your own custom linux OS with all of the required applications. Once you have your bzImage and init.zx you can launch with FOG by creating a custom iPXE menu.
You could use some of the concepts here:
https://forums.fogproject.org/topic/10944/using-fog-to-pxe-boot-into-your-favorite-installer-images
and here:
https://forums.fogproject.org/topic/11194/poc-using-fog-as-a-netboot-server
with the custom linux OS.
Or you could either create or use an existing live OS and pxe boot it using FOG.
There are a number of ways to get a live boot linux OS running on a diskless workstation.