"A poor craftsman blames his tools". Just kidding Jason.
If the Discount AP machine spins and holds RPM, then it's not the machine. But there are certain attachments you might try. At the auctions, they use a wool pad for compounding/heavy polishing. They switch to a foam pad for waxing/light polishing. Usually 3M products. Then for the final coat, to remove swirls, a hand applied glaze is applied in straight lines front to back (some people use a "waffle foam pad" at this stage with good results). Also the wax product should be looked at. They use CarBrite products but they also do mass production and I'm generally not satisfied with their results. I haven't tried Zaino but it sure sounds like good stuff.
I'm a buffing idiot and generally apply wax/polish by hand anyhow. BTW, when did you get married? I didn't know this.