I don't know that any ESC isn't picky about the transmitter end points which can cause these types of issues. In addition, it's usually the low ( zero throttle ) that is the most common one to see a problem with. Having said that... I think you are getting the high throttle fine if that beep was the slow beep they mentioned. If I'm interpreting the instructions correctly... after getting that slow beep, turn off the power to the ESC leaving the throttle on high... then power the ESC on again and lower the throttle to the lowest setting. That should give the long beep they mentioned and you are suppose to power it off again. If that worked, when you power it back on, the calibration should be set.
Ok if it didn't work, the trims for the throttle may have been adjusted or at least need adjusted to reach what the ESC thinks the low setting is. If your trims are digital on your transmitter ( clicky buttons for up/down and not a slider )... repeat the steps and when you get to the setting for the low throttle setting, once you have the stick all of the way down... then start clicking the down trim button. When clicking the trim buttons, always count the number of clicks you press so you can always get back to wherever you started. I would probably just go 10-20 clicks down at first... if that doesn't work, go back up the same number of clicks and then try again going up on the trim the next time.
Some transmitters have screens that allow you to see the values for your channels... if yours has that, use that info in combination with my suggestions to help you let you know where you are in the travel.