Hi Trike, here are a few comments:
* As others have pointed out, motor alignment is very critical. I wonder how many DJI users (Naza, WKM, A2) have this issue without ever knowing because they don't have a black box :highly_amused:
* With my Y6, when running the same props on top and bottom, the motor output differs by around 10-12% (bottom motors work harder). This is normal for a coaxial setup. To make motor outputs more equal, the usual recommendation is to use a bottom propeller that is 1 inch bigger in size or you increase the pitch by one. I'm now using a 11x5 prop on top and a 12x6 prop at the bottom that is cut back to 11inch (both Graupner). The motor output now differs by around 5-6%, which I think is ok.
Your selection of 13x5.5" on top and 12x6.5" on bottom is a little odd, because they 'kind' of behave the same. That's why you still see the bigger difference between top and bottom.
* I'm not sure about the battery placement and if the location is really a problem. I'm using a rail system on my Y6 with the gimbal in front and the battery in the back and it flies very well. It uses only slightly more power when flying FF compared to hover, telling me the motors don't have to work much harder. The angle in FF is still smaller then 30 degrees, so the weight shift and possible pendulum effect, is small. More important is that your CG is correct. But when looking at your battery plate, I think it is way to small to provide a solid battery mount. You are likely using a big battery and it needs to be firmly mounted on a bigger plate with two straps.
* I don't know your dampening system, but often they make things worse in FF. It should only help to avoid jello and some vibrations in the camera, but not more. Soft dampeners work well during slow flight, but have issues with faster flight. Maybe try to tighten things up and try again. I heard from users who even completely removed dampeners and suddenly got much better results. If you are trying to remove jello from a GoPro, then try an ND filter instead. It makes a huge difference.