Actually, all Toyota's CVTs are called "CVTi-S" regardless of the model. It's a brand name standing for "intelligent shift", not sport. All have fake shift points for "sensation" (Toyota's own words) as many people still associate wrongly, by habit, "slipping", "rubber band" or "drone noise" to the fact that a CVT goes right to peak power without needing up/down in revs.If equipped with the paddle shifter option, you can get "personalized" sensation.
From a marketing point of view, it's a success but it goes at the cost of some of the efficiency inherent to a CVT without them. It's not invasive, though. The "sport mode" in the S model basically allow those shift points to occur at higher rpm, thus closer to what a CVT can do (and also modify resistance of the steering wheel). It's always tricky to speak of gears with a CVT. It has none. Not one, not 7, not even infinite. What it has is variable ratio between the configuration of the pulleys.
To answer the original question of the OP, at the cost of a CVT and the work involved, unless you have too much time on your own and enjoy a challenge, it would make more sense financially to take the hit in equity and get a new model.