I have a data logging application in which the processor needs to wake-up using periodically, read sensors, write to non-volatile memory and enter a low power state. Does anyone have any advice on how to shoehorn that paradigm into a multi-tasking application?

The normal thing to do is write an idle hook function that places the micro into low power. That way, every time there are no user tasks running the idle task will automatically put the micro to sleep.

Using the idle task hook you can stop the processor clock in sleep mode using the WFI instruction to wake up on an interrupt. If you're in the idle task there's nothing going on until some kind of interrupt occurs anyway, so it's safe to stop the CPU.

Beyond that you can dynamically reduce the SYSCLK frequency if you know there's no heavy demand for compute cycles. take a look at the STM32 datasheet on power consumption as clock rate decreases. Reduce the PLLCLK multiplier but be sure to keep the SysTick frequency the same by adjusting the count. You can make the task easier by setting up the AHB and APB clocks at a lower frequency so all a PLLCLK/SYSCLK change requires is changing clock prescale values. SysTick is critical because FreeRTOS uses it for scheduling and preemption.

Beyond sleep mode you have to handle the loss of SRAM in deep sleep mode by doing warm restarts, going through the SRAM and peripheral initialization. You can keep application status in the BKP registers to restart at a known point.