A fuel tuner for an 800 would not give you a performance increase like it does for the 900's & 1000's. It would simply be used to increase or decrease fueling and should only be used if something else has changed such as a turbo, or big bore or high flow exhaust etc.
That said, if you were to increase your HP you would rev more. And there are situations where the added HP may put you over the 6500 rev limit. For example a turbo would do this and you would need to add weight to your clutch flyweights to bring the RPM's down back into safe range.
If you have a stock clutch with those bigger tires, an adjustable kit will increase your performance as it gets your RPM's back into a better power range. It is your best bang for the buck.