There is very little damping in the stock 800 fork. If you install heavier and linear springs, the front will still compress too easily and then bounce back up, faster than it does now. Dancing bike.
Better damping is required. That means better components x$ or at least the budget option which is heavier oil.
If you get a better front you might end up wanting a better shock as well. Then you will want better brakes.
A.s.o.
Search s2r800 fork suspension upgrade. It has been discussed.