Is there a way to trigger an interrupt that fires a different method from a UART IRQ?

As I recall you can generate an EXTI or flag a lower priority interrupt in the NVIC itself

Brilliant, at least on your part. It didn't take me long to go from your comment to the fact that since the class that has the control loop calculation method uses a timer, I can set an unused interrupt in that timer to trigger an IRQ that runs the control loop calculation without blocking the UART IRQ.

That's the good news. The bad news is that now that I've implemented this and it seems to work, I realize that all I've done is push the blocking action of doing the control loop calculation from the UART IRQ into the TIMER_TRIGGER IRQ. Still probably a bad practice. Oh well, another seemingly good idea on my part down the tubes.

If case this approach might help someone else, here is what I did:

I put this in the UART RXIdleCallback IRQ (which is where the pressure message gets handled):

HAL_TIM_GenerateEvent(&hBE_CTDTimer, TIM_EVENTSOURCE_TRIGGER);

and this in my timer IRQHandler

if (__HAL_TIM_GET_FLAG(&hBE_CTDTimer, TIM_FLAG_TRIGGER))
{
	timer2HAL_TIMEx_TriggerCallback(&hBE_CTDTimer);
	__HAL_UART_CLEAR_IDLEFLAG(&hUART7); 
}