As I continue to research it seems to me the magic is in whether the devices are "open drain" or "push-pull". I've confirmed that the STM6503 is open drain (active low) and the FT232RL's DTR is push-pull. Since the FT232RL is actually driving the line high in normal operation I have to engineer around this and can't simply connect both to the RESET input.
As long as I'm understanding this correctly, it comes down to this: How do I include an open-drain device to pull RESET low while the FT232RL is holding it high? I'm guessing that's a fairly easy question for someone but I'm not sure how to best approach it. I'm still thinking maybe just a 10K series resistor on the FT232RL's DTR line? Would that screw with its pulse too much to where it wouldn't then be able to reset the AVR?