Tonight I looked over the code and in basically one sitting modified it to a point where I think it should work. The task was really quite easy, actually! The man who wrote it was nice enough to leave extensive comments that were helpful in elucidating the meaning of the complex variable names and mathematical equations. I still don't understand the stuff for drawing circles, but I don't need to modify that code, so who cares? All I really had to do was change the bipolar stepper motor class to use pulses and direction high/low logic rather than using four inputs to manually step through the motor sequence. I also deleted the unhold() function that released the holding power on the motors because I didn't have a way to port that to my EasyDriver setup easily and didn't see it as necessary.
A word of warning - I haven't actually tested this code yet! It is late at night and I have other business to attend to. Hopefully, I can get the code tested soon. I noticed that it doesn't use limit switches at all, so I might be able to improve by adding support for those and potentially also for PWM laser modulation to set the intensity of the laser rather than just going faster/slower to engrave/cut. I didn't bother to post my modded code because it is untested. However, once I test it, I will post some download links.
Lastly, I sacrificed a black foam food container to the hungry red beam of my laser cutter. I made five of drawMrSmiley() cut all the way through the foam. They were pretty sweet looking, but I gave them away to inquisitive people before I photographed them. This foam cut like butter - even more quickly than the craft foam - I almost couldn't go fast enough to prevent a full cut. PWM should help!