A properly setup Genesis RBA will wick easily, but they have their own quirks like cartotanks do. I won't discourage you from investigating RBA's further or even purchasing one to experiment with, but be aware that RBA's have more complexity than a cartotank does and don't work right out of the box like a cartotank can. You will need to learn how to roll your own wick from stainless steel mesh and wrap your own heating coil from wire. You will also need some basic understanding of ohms and resistance and on battery safety measures.
Since you currently are using a cartotank and having some issues with it, lets first focus on that:
What juices are you using (pg/vg ratio) and are you using laser-drilled carts or punching your own holes (how many holes)? You may only need more holes to increase juice to the carto.
What method are you using to pre-fill your cartomizers before putting them in your tank?
Consider your vaping technique. A slow, deliberate, gentle and patient draw of 3-6 seconds length works best to allow proper filling of the cartomizer from the tank. Some of the thicker juices will require you to do some occassional pulls without power on to allow juice to fill the carto.