Does the 144-hour Visa-free Transit in Chengdu cover the whole region of Sichuan?

No, you will not be able to travel throughout Sichuan province because 144 hour visa free transit in Chengdu is limited to the area covered by the city boundaries. In reality, this is quite a large area (14,378.18 km2 - the size of Montenegro), but unfortunately all the three mentioned destinations are outside the city limits. You can precisely see where are the city limits by inserting the name Chengdu in the google search engine and the results presented on the upper right hand side will present the small map of Chengdu. Just click on the map and when enlarged you will see the exact boundaries of Chengdu city marked with red line.