Hey, I think I found your lathe auction:
http://www.ebay.com/itm/SB1002-Sout...D&orig_cvip=true&rt=nc&_trksid=p2047675.l2557
I didn't know they sold tent-sale items on Ebay!
The trouble with this kind of stuff is that it looks cheap at first, but when you need to buy a chuck, magnetic switch, etc then the costs mount up quickly. Then you get this:
NO PARTS
NO WARRANTY
NO RETURNS
Which makes the initial repairs kind of hurt. At this point, however, that's water-under-the-bridge. You can either cry in your Cheerios or just fix it. Luckily, the spindle is driven solely from stepped pulleys. You can't get any simpler than that as this lathe doesn't have back gears/cone pulley. You can make this lathe work correctly.
First you need to make sure you tachometer is working correctly. Some of the cheap ones don't like a fluorescent lights, so verify your equipment on a known RPM. Tach verified OK? Time to move on.
I'll assume your rpm data is correct in the chart you attached. The motor is shown at 1200 RPM which is correct, but all the other speeds are WAY TO HIGH! On the highest pulley speed (in low) you are getting 601 RPM. If you actually got high speed to work without binding the crap out of pulleys, the spindle speed would be 3300 RPM, when it's supposed to top-out at 1200 RPM. No wonder you're bogging the motor.
The chart isn't wrong, the chart has the speeds that you need and you need to make the lathe work at those speeds. Luckily, as you said, it's just Jr High calculations. Since the motor is spinning at the correct speed and everything else is fast, then either the step pulley on the motor is wrong, the pulley that it drives is wrong, or they both are wrong. Since this lathe was obviously some kind of test mule this isn't surprising. This would also explain the binding your describe in high: wrong pulley(s).
You paid extra for a lathe without a new fangled VFD or other electronic controller, so stick with the pulleys and make them work.
If it was me, I would carefully measure the diameter of each pulley step and then contact Grizzly and see if they can tell you which of the pulleys is wrong. Maybe you can shame them into a replacement. Having stuff missing is one thing, but totally wrong components is a bit much.