Below is a screenshot from one of the TI C2000 TSP demo models. The model uses the approach you describe - in the bottom left of the schematic a digital input is used to toggle the PWM signals going to the switch. If the signal is low, then all PWM signals are zero, and the average on-time for all switches is zero is as well. If the signal is 1, then the PWM signals connect to the component gates as expected.
Multiplying by the digital input signal would have a similar impact. Can you be specific on why that approach doesn't seem to work for you?
You can download the TI C2000 TSP from the Plexim website (https://www.plexim.com/download/tsp_c2000) and explore the demo models - most of them implement a similar logic.