First off, it would probably be better to actually use a linear flight plan to collect that data.
From the Flat Maps article:
"Flat Maps do not rely on matching features from a bunch of different angles to give an answer the way photogrammetry does. Flat Maps use the camera's pointing angles and sensor/lens parameters combined with our terrain data to find out where the images were taken of to provide a quick and dirty output that is used to fill in the gaps."
Basically the Flat Map will only be as good as the tags the camera provides. GCPs won't fix this issue.
Flat Maps require less overlap because there is zero matching that goes on. If you want everything to line up perfectly you should be using the regular photogrammetric process but that requires 75+% overlap to work.
Looking at your account I see you are basically only doing Flat Maps but it sounds like that might not be what you want. You have an Elite subscription so you can process up to 400 images for free. You just need to collect more data.