everyone on here is giving good advice, and your not doing anything wrong, sometimes you get great results and sometimes you don't. the only things i could suggest for your situation, since your current set up isn't working as well for you as you'd like are not to transplant into peat. Peat isn't bad, as I'm germinating in peat right now, but (i will not say it is better but) it is SAID that smaller plants like lighter soil, peat retains a lot of moisture and can be heavy. TRY transplanting into a different medium or a starter soil mixed with perlite and vermiculite. Approximate 1 part perlite, 1 part vermiculite, to 4 parts seeds starting soil. Transplant into 5-8oz clear plastic cups (I like clear because i like to see when the roots become visible root bound so i can transplant to a bigger pot asap, it's also easy to see moisture levels in the clear cups), cut drain holes in the bottom and water heavily the first time, always wait until the moisture level is about halfway down the cup before rewatering. When you start to see signs of roots growing along the sides of the cup, it's safe to transplant up to say a 6" pot or so and probably old enough to get hardened off. This is just the way I always go through my baby-toddler stages of Capsicums.