Hmmmh, CVTs are simple but sophisticated transmissions, where several components compliment or fight each other.
As you say, theoretically should work....
Not to tell from distance.
Your counterspring behind your clutch is a factor too, that's why MALOSSI delivers new CVTs with a set of them.
Yes, a worn out (too small) belt cannot transfer performance.
A new belt, BANDO or MITSUBOSHI might be a good idea.
It's an interesting field, there are zillions of videos around.
If you do have some money left over, try Dr.PULLEYs or TechPülley squares/gliders.
BANDO rollers are fine too and last.
A very important step IMO is to polish the CVTs inner ramps. NO lube at all there.