I don't want to add an SD card
Why not? They are relatively cheap, and are the easiest way to share text between an Arduino and a PC.
My second thought was to plot the cures and fit a polynomial and use that but the iteration time for that could be quite slow
If you are using AccellStepper to move 6 steppers at once, most of the time the Arduino is doing nothing more than waiting fro the steppers to get where they are going. You can use that time to be computing the next position(s).