It may sound radical, but the best way to keep your feet on the pedals is with toe clips. Before you dismiss this as something that would never work, consider the steps to make this possible. I have ridden with toe clips for over 20 years, on everything from a 24" to a giraffe to my new Coker D.
You can get toe clips at your local bike shop if you don’t have an old pair lying around. Begin by putting the toe clips on your uni pedals without the straps. You can even put a clip on only one pedal to begin with. Your feet will still come off the pedal if you fall off, but the clip will make you a little more sure-footed. Try this for several rides, and once you feel comfortable with them you can add straps. I leave the straps very loose unless I am jumping steps.
The term toe clip should not be confused with clipless pedals found on a mountain or road b***. Your feet don’t “clip” to the pedal with a toe clip, they just slide in. You may want to try toe clips with a smooth pedal, since a pedal with pins would hold your foot tighter. Many pedals have flat edges (sides) that will allow a toe clip to be secured to it with a couple of bolts. I got my last set of pedals, toe clips, & nylon straps from www.performancebike.com, but again, your local shop should have them in stock.
Again, it may sound dangerous, but so did wheel-walking or one-foot riding until you spent some time on it. Let me know if you have any questions.