Hi-

Sounds like you are doing great so far! I'm not sure about using both types of peat at the same time. I probably wouldn't do it that way. Are these going in a bigger planter or into the ground next? This will also alter the answer as to what to put them in next, as even though it may have true leaves, the roots may or may not even need more space yet, and could be closer to hardening off than putting it into another layer away from the soil it will be in next. 

Here are some reading materials that may help give you some insight into next steps and some options:

https://hgic.clemson.edu/factsheet/starting-seeds-indoors/

https://extension.uga.edu/publications/detail.html?number=B1432

https://extension.okstate.edu/fact-sheets/print-publications/hla/growing-vegetable-transplants-hla-6020.pdf  "Another consideration when using compressed peat pots is the edges of the pot should not be allowed to be above the soil surface after planting. It will act as a wick and pull moisture away from the transplant."

I hope this helps. Also, unless something says otherwise based on your next step, I would continue to bottom water.