Hi Oli,
the time base, even if CubeMX says it's not recommend to use SYSTICK therefore, is correct. We do not really know why STM32CubeMX wouldn't allow that but on the other side in ST examples this is totally normal...
A couple of months ago I had prepared a STM32CubeMX project for the STM32F746G Discovery, you can find it here. Clearly it wasn't made for the same controller, but basically the STM32CubeMX workflow is quite similar. Even in that project the FreeRTOS warning appears, but the OS it works anyway.
Unfortunately this conversation here is a bit uncompleted, cause the rest of the it was in our email exchange. As I already wrote there, I'm assume the problem is caused by a wrong task priority setup.
So, have you seen this thread here? It often happens that FreeRTOS tasks can block each other...
Best regards,
Tim