Configuring the rate of Timer interrupts for the STM32F4xx Discovery Board
So after much frustration I figured out how to scale my timer/interrupt. I was trying to do it all at once instead of develop it incrementally.

In case anyone finds this question I found this article and followed its step by step instructions - configuring the timer, then the interrupt, then the interrupt handler. I think my issue was that I was not clearing the Pending Bit after each interrupt, as they do in step 9:

TIM_ClearITPendingBit(TIM2, TIM_IT_Update);


Adding that to the end of my interrupt handlers seemed to do the trick. I can scale timing as I would expect to by providing variable arguments to the prescalar and period.