I've never heard of using bungee cords to offset a spindle's weight, and it doesn't sound like a good idea. Cords like that - or any tension spring - won't offset weight evenly; it's not enough to start with, and too much at the extremes of tension. I've tried constant-force springs, which worked as long as they lasted, but that wasn't very long. What worked best for me was gas struts, which exert a more linear force no matter where in the stroke they are. Another solution I've heard people use (but haven't tried myself) is a counterweight, which is less convenient to rig but also linear.
Those motors you're using have very high inductance, which means that they need a lot of power supplied to work efficiently. The formula 32 * (sq.rt.of) inductance = optimum max power input says those motors want about 86 volts to run at their best; at 30v it's not surprising they're faltering and easily stopped by hand. The fact that you're only giving them about half the current they want (1.5 amps vs. 2.83) isn't helping either.
If you want to keep using those motors, throw out all that arduino grbl junk and the Pololou drivers (or keep them for building a 3D printer, using much smaller motors) and buy 3 Gecko V203 drives http://www.geckodrive.com/g203v.html which can handle 80v and more current than you need. Get a power supply that can put out 80v and enough current (I like these: PS-10N80 - 1000W 80V Power Supply - AnTek Products Corp ) and that machine of yours will fly. Yes, it will cost some money, but isn't all that walnut starting to add up - not to mention the time you're spending tearing your hair out?
If you want to use James Newton's THB6064 drives, get some motors with less inductance that will work best at 50v or so and a power supply to match. Mach3 is totally worth the money, but if you can't spend it, go with LinuxCNC, which is free.