I seriously doubt that a new cable is going to help.
I suspect that what you are experiencing is commonly referred to as "clutch drag". This is usually caused by a certain amount of "fluid coupling".
The clutch is made up of a stack of plates. Have the plates are connected to the engine output shaft while the other half (every other plate) is coupled to the transmission. The pressure plate may move 1/2" off (mine doesn't move that far...) but that space has to be divided between all the plates, which doesn't leave much space between a plate that is spinning with the engine and the plates that are stationary with the transmission.
Now you pour some oil into this equation. The oil fills the gap between the two plates and couples them together. The thicker the oil is, the more the coupling.
There are other factors that can enter into the equation as well. If the clutch has ever been overheated (excessive slipping) then it is possible that the clutch plates warped. If one or more plates have warped then it is possible that you still have friction contact between the plates.
I would expect the problem to be worse when the engine is cold and the oil is thicker.
Gear oil is measured on a different scale than motor oil. An 80 wt gear oil is somewhere between 20wt and 30wt motor oil so it is possible that by switching to 30 wt you actually an even thicker oil, which would make your problem worse.
I run a 5wt synthetic oil in my bikes, which helps a lot. I recommend trying that first, and if that doesn't help then consider changing the clutch out.
Rod