I’d suggest using the softest light possible. If by flood lights you mean regular work lights, you’ll need to diffuse them. Even hanging a sheet of paper in front (not too close – don’t want it to catch fire) to diffuse the light. Anything really that is white and semi-opaque – paper, fabric, ect. Also, when using your flash, if the ceiling is low enough (approx. 10 feet or less), bounce the flash off of the ceiling for diffusion or just use a diffuser on your flash. That should drastically reduce your shadows.
Just do some googling on light diffusion and you should find plenty of guides.
Worst case scenario you could cut the pieces out since I’m assuming you’re using a solid colored background. You can add some shadows yourself if you want to make it look less cut out.