Might I advise you against what you are about to do?
I'm new to the forum, but not new to the hobby. Been in it about 20 years now and I would love to help you figure this all out.
Already I can see some issues that might arise from your set up. You mentioned that you tried planting before, and were met with mass browning. Do you know why this happened?
You also mentioned that you don't want to dose Co2 and avoid mass fertilizing. Is there any way I can change your mind on this?
Planted tanks require both macro and micro nutrients to survive and grow. Two frogs aren't going to provide a 20g filled with plants with enough nutrients to even survive, let alone carpet the floor.