So the Mesa 7i77 should control those drives and read the encoders. Then as you say, you let the motion controller (linuxcnc) manage the feedback loop. Here is a tutorial on drive tuning by BigJohnT mentioned above.
https://gnipsel.com/linuxcnc/tuning/servo.html
Your best bet is to grab some photos of your drives and motors (part numbers too if you can find them) and post on the Linuxcnc forum. I don't really have the experience to guide you here but plenty of others wiull help.