Hyundai 18s hit sinumerik 840c

So it looks like you are well documented. Nice, that will save you hours trying to follow the wiring around the machine.
I can just barely read it but that is the coolant and hydraulics. On the right are the drives but only the over view. Maybe a bit further you will find the servo motors.

Well, while I think it may well be possible to get this machine back up and running with LinuxCNC I don't think you will get this done in 2 weeks.

The mesa boards: eusurplus.com/index.php?route=product/search&search=7i77
Delivery has always been very fast for me (2-3days). But then those need to be wired and then the configuration will need to be set up.
Impossible to say how much time that will take. If you have somebody who knows the boards and LinuxCNC and everything works together then 2 weeks might actually be realistic but if you need to learn the system as you go then it will take a lot longer.
In any case, since you have all the documentation, you would want to get a clear concept of how things are going to be connected to the mesa boards. Position feedback to linuxCNC is the first that would need to be clear (The 7i77 needs encoder inputs if I am not mistaken) May be your drive provides a simulated encoder output to feed back to LinuxCNC but I don't know.

Note that the user in the thread I posted earlier seems to have added incremental encoders to the motors as a feedback to the 7i77 and LinuxCNC