Based on the symptoms and difficulties to reproduce, I think what you see on the screenshots are incomplete renders. The FF code submitted some draw calls to GPU, and copied the render target texture without waiting for draw calls to complete. A good way to fix is use a D3D11_QUERY_EVENT query to wait for completion of rendering.
If all GPU access happens through D3D11 this shouldn’t happen i.e. the API guarantees to wait for the completion of previously submitted draw calls. It may happen in practice when mixing multiple GPU APIs, e.g. when using DXGI surface sharing to pass textures between D3D11 and DX9. Also, it may happen when using D3D from multiple threads. Easy way to detect the latter, set D3D11_CREATE_DEVICE_DEBUG flag when creating the device, and read warnings in debug output of the process.
Another possibility is just bugs in rendering code. To troubleshoot them, https://renderdoc.org/ is awesome. Unfortunately, if the FF doesn’t use D3D to present, only rendering to textures, some changes to FF’s source code is required to capture frames with RD, see this page for details: https://renderdoc.org/docs/in_application_api.html