Feet on the middle of the pedals
If I understand the problem correctly, it sounds like you're sitting too far forward on this bike. Whether you're too tall for your frame or not is difficult to diagnose without at least pictures, but you might consider that this bike is simply too small for you. (If you're having trouble getting the handlebars far enough forward, that's a sign that this could be the case.) Are you able to get the saddle high enough so your knees are locked with the heel of your foot on the pedal? 

You might also consider simply moving your saddle back on the rails. That might give you a little more room. 

I'd also repeat Wadelp's suggestion - toe clips will help you keep your feet correctly positioned on the pedals.