I think the concept of transplant shock gets a bit overdone. Auto or not, that plant looks overgrown for the pot, the root ball must be quite hearty by now, and the biggest risk of transplant shock is actually a weak rootball, so you should be pretty safe! Just wait for it to dry out nearly to the point of wilt
(This seriously reduces chance of root damage), get your big pot ready, lace your fingers over the soil surface around the stem, flip it completely upside down, and give the bottom of the cup a sharp smack.
Water lightly in the new pot and give just enough water to keep it perky forcyge first week or so, then you can go back to normal watering.
Fresh soil is a real treat for a potbound plant and exposing the whole root ball to it will encourage your roots to spread efficiently!