Hi S., good for you for trying the cloth diapers. The environment really thanks you :-) When my son was at your sons' age, I used the Bummis Whisper Wraps and now he is using Bummis Super Snap (he is 13 mos now). I also use non-bleached prefolds. I doubt that your Superbrites are much different as far as the cover goes. I use cloth about 95% of the time - using a chlorine free disposable at night and occassionally when we are out running longer errands. I can honestly tell you that I've had far more leaks with the disposables than the cloth. So cloth will work for you very well once we figure out the root of the problem.
The first thing that really jumped out at me in your question is that you only change them every 3 hrs. Of course they are completely saturated. I change my son every hour that he is awake (and upon awakening from his naps). When he was one month old, I normally found saturated diapers as well..and that was every hour. I took that as a good sign that he was drinking enough. So you should be happy that your boys are eating/drinking well. Only recently, do I check him and find that he sometimes still dry since the last change. One month olds average about 12 wet diapers each day(or maybe 10 disposables if I remember what I've read). The cloth is natural and does not contain all the chemical gels that absorb the urine and allow you to go 3 hrs between diaper changes. You need to change cloth diapers more than you would a disposable. I think the three hours between changes is a big part of your bad experience with leaks.
Also, you are correct that the diaper must be completely inside of the cover. It does makes sense that if a wet diaper is sticking out of a cover that whatever it touches will also become wet. I do remember that when my son was only a month..it was harder to fit the diaper in the cover...since the diapers are pretty much always the same size, but the covers are so small. When my son was your sons' age, I folded the diaper by folding up about 4" from the bottom and then folded both sides to the center. That normally made it to where the diaper would lay completely centered in the cover/the entire length of the cover w/o going over. The side that I folded up from the bottom (kind of doubled-up) was what I used in the front to give him that extra layer of absorbency. Eventually as he grew into larger covers, the diaper can now only be folded in one strip (two sides folded to center).
Also, I remember when I first purchased the diapers, I was supposed to wash them several times in Hot water before using them the first time. This was supposed to break down the natural oils in the coton and increase their absorbency. I suspect after a month of use, you have washed them many times already..so this probably is not your problem. However, if you are not using low-residue detergents (like Charlie's Soap etc) you may be experiencing issues with your detergent leaving residue on your diapers which coat them and cause the liquid to "pill" and run instead of absorb. I believe I read the recommended washing methods/detergents in the literature that came with the bummmis, so you may have already read/covered this piece. If not, I know its on their website. Good luck and feel free to ask me additional questions on the Bummis and I will try and help you.