I think most folks suggest up-planting a couple of times so there is a lesser amount of soil which reduces the tendency to over-water. Conversely, auto plants have a short life and short recovery times, so multiple up-plants is not often suggested for autos. I start an auto in a solo cup, then up-plant in the final home...so I am limiting my plant's shock exposure.
Now you realize your plant is actually a photo, this opens the door for up-plant opportunity. Some folks use smallish containers even for larger sativa photo plants. I realize you want to transplant, and by all means follow your inclination to put the plant in a larger container. Conversely, you may not get a huge yield increase based on the current size and age of the plant....but then again you may. There's always risks when you transplant, and if all is good as is, you may want to carefully evaluate the risks.