Try this with the wheelie. Once you get the heads reasonably sharp, push them through from the front, angles upwards (opposite angle than pulling them through). This is with very light pressure. That is a tip I got from ChuckC, it works. I have used the wheelie on a bunch of simmons heads and it is quick and easy, though I have switched to Chris Spikes method. I know you don't want to buy more stuff, but the jewelstick and edge guide are for and away the best method, in my opinion. I have also used it to sharpen all my knives as well. Good luck, and let us know of you need more help.
Jake