Adding fins to IS Blue Lake Quad Fin?

We are beginning wakesurfers with an IS 2008 Blue Lake Quad Fin board. We are getting up and getting some slack in the rope but haven't been two successful on sustained runs without the rope. We have had experienced wakesurfers ride behind our boat successfully (with their own board and the Blue). So, I believe our wake is sufficient. Sorry, no photos.

We are still learning technique. The goal for now is to get us "cruising" in the pocket for longer. However, I am not opposed to leveraging technology/equipment to speed this process along. The board comes stock with two fins but will support four. If I understand correctly, we can add two more fins (inner slots) and this will help with thrust (sacrificing some spinning/maneuverability). Is this correct? If so, would this make it easier to stay in the pocket longer?

If yes, then what fins would be recommended? IS makes a couple of different types. Are there also 3rd party companies who make fins?

Thanks in advance!